Xiaolei Fang, Meiqing Liu, Jinquan Luo
In this paper, we propose a mechanism on the constructions of MDS codes with arbitrary dimensions of Euclidean hulls. Precisely, we construct (extended) generalized Reed-Solomon(GRS) codes with assigned dimensions of Euclidean hulls from self-orthogonal GRS codes. It turns out that our constructions are more general than previous works on Euclidean hulls of (extended) GRS codes.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
The Galois hulls of linear codes are a generalization of the Euclidean and Hermitian hulls of linear codes. In this paper, we study the Galois hulls of (extended) GRS codes and present several new constructions of MDS codes with Galois hulls of arbitrary dimensions via (extended) GRS codes. Two general methods of constructing MDS codes with Galois hulls of arbitrary dimensions by Hermitian or general Galois self-orthogonal (extended) GRS codes are given. Using these methods, some MDS codes with larger dimensions and Galois hulls of arbitrary dimensions can be obtained and relatively strict con…
The hull of a linear code is the intersection of itself with its dual code with respect to certain inner product. Both Euclidean and Hermitian hulls are of theorical and practical significance. In this paper, we construct several new classes of MDS codes via (extended) generalized Reed-Solomon (GRS) codes and determine their Euclidean or Hermitian hulls. Specifically, four new classes of MDS codes with Hermitian hulls of flexible dimensions and six new classes of MDS codes with Euclidean hulls of flexible dimensions are constructed. For the former, we further construct four new classes of enta…
The hull of linear codes have promising utilization in coding theory and quantum coding theory. In this paper, we study the hull of generalized Reed-Solomon codes and extended generalized Reed-Solomon codes over finite fields with respect to the Euclidean inner product. Several infinite families of MDS codes with arbitrary dimensional hull are presented. As an application, using these MDS codes with arbitrary dimensional hull, we construct several new infinite families of entanglement-assisted quantum error-correcting codes with flexible parameters.
In this paper, we construct several classes of maximum distance separable (MDS) codes via generalized Reed-Solomon (GRS) codes and extended GRS codes, where we can determine the dimensions of their Euclidean hulls or Hermitian hulls. It turns out that the dimensions of Euclidean hulls or Hermitian hulls of the codes in our constructions can take all or almost all possible values. As a consequence, we can apply our results to entanglement-assisted quantum error-correcting codes (EAQECCs) and obtain several new families of MDS EAQECCs with flexible parameters. The required number of maximally en…
We define the Euclidean hull of a linear code $C$ as the intersection of $C$ and its Euclidean dual $C^\perp$. The hull with low dimensions gets much interest due to its crucial role in determining the complexity of algorithms for computing the automorphism group of a linear code and checking permutation equivalence of two linear codes. It has been recently proved that any $q$-ary $[n,k]$ linear code with $q>3$ gives rise to a linear code with the same parameters and having zero dimensional Euclidean hull, which is known as a linear complementary dual code. This paper aims to explore explicit …
The hull of linear codes plays an important role in quantum information and coding theory. In the present paper, by investigating the Galois hulls of generalized Reed-Solomon (GRS) codes and extended GRS codes over the finite field Fq, we give several new families of MDS codes with Galois hulls of arbitrary dimensions that are not obtained before. Some of them generalize the ones in the literature [13]. As a consequence, using these MDS codes with Galois hulls of arbitrary dimensions, we construct nine new families of MDS entanglement-assisted quantum error-correcting codes (EAQECCs) with flex…
The hull of a linear code is defined to be the intersection of the code and its dual. When the size of the hull is small, it has been proved that some algorithms for checking permutation equivalence of two linear codes and computing the automorphism group of a linear code are very effective in general. Maximum distance separable (MDS) codes are codes meeting the Singleton bound. Twisted Reed-Solomon codes is a generalization of Reed-Solomon codes, which is also a nice construction for MDS codes. In this short letter, we obtain some twisted Reed-Solomon MDS codes with one-dimensional hull. More…
We prove that any Hermitian self-orthogonal $[n,k,d]_{q^2}$ code gives rise to an $[n,k,d]_{q^2}$ code with $\ell$ dimensional Hermitian hull for $0\le \ell \le k$. We present a new method to construct Hermitian self-orthogonal $[n,k]_{q^2}$ codes with large dimensions $k>\frac{n+q-1}{q+1}$. New families of Hermitian self-orthogonal codes with good parameters are obtained; more precisely those containing almost MDS codes. By applying a puncturing technique to Hermitian self-orthogonal codes, MDS $[n,k]_{q^2}$ linear codes with Hermitian hull having large dimensions $k>\frac{n+q-1}{q+1}$ are al…
The MDS or NMDS for Modified GRS codes with flexible hull dimensions and lengths
研究修正广义Reed-Solomon码及其扩展码的MDS/NMDS性质，确定NMDS条件与权重分布，构造欧几里得LCD码和Hermitian壳码，并证明其线性不等价性。
Let $\mathrm{SLAut}(\mathbb{F}_{q}^{n})$ denote the group of all semilinear isometries on $\mathbb{F}_{q}^{n}$, where $q=p^{e}$ is a prime power. In this paper, we investigate general properties of linear codes associated with $σ$ duals for $σ\in\mathrm{SLAut}(\mathbb{F}_{q}^{n})$. We show that the dimension of the intersection of two linear codes can be determined by generator matrices of such codes and their $σ$ duals. We also show that the dimension of $σ$ hull of a linear code can be determined by a generator matrix of it or its $σ$ dual. We give a characterization on $σ$ dual and $σ$ hull…
On Linear Codes Whose Hermitian Hulls are MD
针对 Hermitian 包络本身为 MDS 的线性码刻画难题，本文提出研究工具与显式构造，覆盖 Reed–Solomon 型和非 Reed–Solomon 型 MDS 码，并在相同包络维数下获得更高码维。
In this paper, a criterion of MDS Euclidean self-orthogonal codes is presented. New MDS Euclidean self-dual codes and self-orthogonal codes are constructed via this criterion. In particular, among our constructions, for large square $q$, about $\frac{1}{8}\cdot q$ new MDS Euclidean (almost) self-dual codes over $\F_q$ can be produced. Moreover, we can construct about $\frac{1}{4}\cdot q$ new MDS Euclidean self-orthogonal codes with different even lengths $n$ with dimension $\frac{n}{2}-1$.
In this paper, we construct MDS Euclidean self-dual codes which are extended cyclic duadic codes. And we obtain many new MDS Euclidean self-dual codes. We also construct MDS Hermitian self-dual codes from generalized Reed-Solomon codes and constacyclic codes. And we give some results on Hermitian self-dual codes, which are the extended cyclic duadic codes.
The study of MDS self-dual codes has attracted lots of attention in recent years. There are many papers on determining existence of $q-$ary MDS self-dual codes for various lengths. There are not existence of $q-$ary MDS self-dual codes of some lengths, even these lengths $< q$. We generalize MDS Euclidean self-dual codes to near MDS Euclidean self-dual codes and near MDS isodual codes. And we obtain many new near MDS isodual codes from extended negacyclic duadic codes and we obtain many new MDS Euclidean self-dual codes from MDS Euclidean self-dual codes. We generalize MDS Hermitian self-dual …
The parameters of a $q$-ary MDS Euclidean self-dual codes are completely determined by its length and the construction of MDS Euclidean self-dual codes with new length has been widely investigated in recent years. In this paper, we give a further study on the construction of MDS Euclidean self-dual codes via generalized Reed-Solomon (GRS) codes and their extended codes. The main idea of our construction is to choose suitable evaluation points such that the corresponding (extended) GRS codes are Euclidean self-dual. Firstly, we consider the evaluation set consists of two disjoint subsets, one o…
Recently, the construction of new MDS Euclidean self-dual codes has been widely investigated. In this paper, for square q, we utilize generalized Reed-Solomon (GRS) codes and their extended codes to provide four generic families of q-ary MDS Euclidean self-dual codes. In particular, for large square q, our constructions take up a proportion of generally more than 34% in all the possible lengths of q-ary MDS Euclidean self-dual codes, which is larger than the previous results. Moreover, two new families of MDS Euclidean self-orthogonal codes and two new families of MDS Euclidean almost self-dua…
The Galois hull of a linear code is the intersection of itself and its Galois dual code, which has aroused the interest of researchers in these years. In this paper, we study Galois hulls of linear codes. Firstly, the symmetry of the dimensions of Galois hulls of linear codes is found. Some new necessary and sufficient conditions for linear codes being Galois self-orthogonal codes, Galois self-dual codes, and Galois linear complementary dual codes are characterized. Then, we propose explicit methods to construct Galois self-orthogonal codes of larger length from given Galois self-orthogonal co…
The intersection ${\bf C}\bigcap {\bf C}^{\perp}$ (${\bf C}\bigcap {\bf C}^{\perp_h}$) of a linear code ${\bf C}$ and its Euclidean dual ${\bf C}^{\perp}$ (Hermitian dual ${\bf C}^{\perp_h}$) is called the Euclidean (Hermitian) hull of this code. It is natural to consider the hull-variation problem when a linear code ${\bf C}$ is transformed to an equivalent code ${\bf v} \cdot {\bf C}$. In this paper we introduce the maximal hull dimension as an invariant of a linear code with respect to the equivalent transformations. Then some basic properties of the maximal hull dimension are studied. We p…
MDS multi-twisted Reed-Solomon codes with small dimensional hull
该研究得到多扭Reed-Solomon码为MDS码的充要条件，提出一类新的MDS双扭Reed-Solomon码并给出示例与计数结果，同时推导了小维数包络的相关存在条件。
Systematic constructions of MDS self-dual codes is widely concerned. In this paper, we consider the constructions of MDS Euclidean self-dual codes from short length. Indeed, the exact constructions of MDS Euclidean self-dual codes from short length ($n=3,4,5,6$) are given. In general, we construct more new of $q$-ary MDS Euclidean self-dual codes from MDS self-dual codes of known length via generalized Reed-Solomon (GRS for short) codes and extended GRS codes.
Three classes of propagation rules for generalized Reed-Solomon codes and their applications to EAQECCs
本文研究广义里德-所罗门码的厄米特壳，通过三种传播规则构造任意维数厄米特壳的MDS码，并应用于获得参数灵活的MDS EAQECCs。
Linear codes with complementary duals (abbreviated LCD) are linear codes whose intersection with their dual is trivial. When they are binary, they play an important role in armoring implementations against side-channel attacks and fault injection attacks. Non-binary LCD codes in characteristic 2 can be transformed into binary LCD codes by expansion. On the other hand, being optimal codes, maximum distance separable codes (abbreviated MDS) have been of much interest from many researchers due to their theoretical significant and practical implications. However, little work has been done on LCD M…
Construction of MDS Euclidean Self-Dual Codes via Multiple Subsets
本文致力于通过GRS码及其扩展码构造新的MDS欧氏自对偶码，提出从多个相交子集中选择求值集的方法，并基于范数函数和乘法子群及其陪集的并集构造了六类新码，使可能的码比例超过85%。
The intersection ${\bf C}\bigcap {\bf C}^{\perp_H}$ of a linear code ${\bf C} \subset {\bf F}_{q^2}$ and its Hermitian dual ${\bf C}^{\perp_H}$ is called the Hermitian hull of this code. A linear code ${\bf C} \subset {\bf F}_{q^2}$ satisfying ${\bf C} \subset {\bf C}^{\perp_H}$ is called Hermitian self-orthogonal. Many Hermitian self-orthogonal codes were given for the construction of MDS quantum error correction codes (QECCs). In this paper we prove that for a nonnegative integer $h$ satisfying $0 \leq h \leq k$, a linear Hermitian self-orthogonal $[n, k]_{q^2}$ code is equivalent to a linea…
In this paper, we study Euclidean and Hermitian hulls of generalized Reed-Solomon codes and twisted generalized Reed-Solomon codes, as well as the Hermitian hulls of Roth-Lempel typed codes. We present explicit constructions of MDS and AMDS linear codes for which their hull dimensions are well determined. As an application, we provide several classes of entanglement-assisted quantum error correcting codes with new parameters.
Galois hulls of linear codes have important applications in quantum coding theory. In this paper, we construct some new classes of (extended) generalized Reed-Solomon (GRS) codes with Galois hulls of arbitrary dimensions. We also propose a general method on constructing GRS codes with Galois hulls of arbitrary dimensions from special Euclidean orthogonal GRS codes. Finally, we construct several new families of entanglement-assisted quantum error-correcting codes (EAQECCs) and MDS EAQECCs by utilizing the above results.
The Euclidean hull of a linear code $C$ is the intersection of $C$ with its Euclidean dual $C^\perp$. The hull with low dimensions gets much interest due to its crucial role in determining the complexity of algorithms for computing the automorphism group of a linear code and checking permutation equivalence of two linear codes. The Euclidean hull of a linear code has been applied to the so-called entanglement-assisted quantum error-correcting codes (EAQECCs) via classical error-correcting codes. In this paper, we consider linear codes with one-dimensional Euclidean hull from algebraic geometry…
Hermitian Hulls of Rational Algebraic Geometry Codes and Applications in Quantum Codes
本文通过代数几何码的埃尔米特包络维度研究，设计出新的MDS EAQECC家族，并验证其参数新颖性。
We construct MDS Euclidean and Hermitian self-dual codes over large finite fields of odd and even characteristics. Our codes arise from cyclic and negacyclic duadic codes.
Localizing a cloud of points from noisy measurements of a subset of pairwise distances has applications in various areas, such as sensor network localization and reconstruction of protein conformations from NMR measurements. In [1], Drineas et al. proposed a natural two-stage approach, named SVD-MDS, for this purpose. This approach consists of a low-rank matrix completion algorithm, named SVD-Reconstruct, to estimate random missing distances, and the classic multidimensional scaling (MDS) method to estimate the positions of nodes. In this paper, we present a detailed analysis for this method. …
Hermitian hull of some GRS codes and new EAQMDS codes
本文将一类广义 Reed–Solomon 码的 Hermitian 包络维数计算转化为格计数问题，给出显式公式，并据此构造具有新参数的多种 EAQMDS 码。
On Iso-Dual MDS Codes From Elliptic Curves
本文证实了Han和Ren关于等距自对偶MDS椭圆曲线码的猜想，提出两种基于椭圆曲线的构造方法，给出码长上界并分析hull维数，最终得到两类新的MDS纠缠辅助量子纠错码。
Let $q=p^h$ be a prime power and $e$ be an integer with $0\leq e\leq h-1$. $e$-Galois self-orthogonal codes are generalizations of Euclidean self-orthogonal codes ($e=0$) and Hermitian self-orthogonal codes ($e=\frac{h}{2}$ and $h$ is even). In this paper, we propose two general methods to construct $e$-Galois self-orthogonal (extended) generalized Reed-Solomon (GRS) codes. As a consequence, eight new classes of $e$-Galois self-orthogonal (extended) GRS codes with odd $q$ and $2e\mid h$ are obtained. Based on the Galois dual of a code, we also study its punctured and shortened codes. As applic…
Galois self-orthogonal MDS codes with large dimensions
本文给出 GRS/EGRS 码及其扩展码 Galois 自正交的充要条件，分类构造维度更大的新 Galois 自正交 MDS 码，并导出任意维度 Galois hull 的 MDS 码及量子码。
Galois Hulls of Generalized Roth-Lempel Codes and Their Applications to EAQECCs
本文提出基于归一化拉格朗日系数的通用方法，构造具有指定Galois壳维数的广义Roth-Lempel码，并应用于纠缠辅助量子纠错码，获得MDS/AMDS码及最大纠缠EAQECCs。
On Construction of Linear (Euclidean) Hull Codes over Finite Extensions Binary Fields
本文提出了一种在有限扩展二元域上构造线性码围包的方法，展示了如何通过弱条件将线性码的围包维度从$ \ell $扩展到$ \ell + 1 $，并推导了相关构造方法。
In this work, we study and determine the dimensions of Euclidean and Hermitian hulls of two classical propagation rules, namely, the direct sum construction and the $(\mathbf{u},\mathbf{u+v})$-construction. Some new criteria for the resulting codes derived from these two propagation rules being self-dual, self-orthogonal, or linear complementary dual (LCD) codes are given. As an application, we construct some linear codes with prescribed hull dimensions, many new binary, ternary Euclidean formally self-dual (FSD) LCD codes, and quaternary Hermitian FSD LCD codes. Some new even-like, odd-like, …
Both linear complementary dual (LCD) codes and maximum distance separable (MDS) codes have good algebraic structures, and they have interesting practical applications such as communication systems, data storage, quantum codes, and so on. So far, most of LCD MDS codes have been constructed by employing generalized Reed-Solomon codes. In this paper we construct some classes of new Euclidean LCD MDS codes and Hermitian LCD MDS codes which are not monomially equivalent to Reed-Solomon codes, called LCD MDS codes of non-Reed- Solomon type. Our method is based on the constructions of Beelen et al. (…
Hull Variation in Symplectic Linear Codes
该研究探讨辛线性码在保持辛距离的等价变换下的核维数变化，引入偶值不变量$\triangle(C)$，推导最小辛核维数公式，证明偶维辛MDS码单项式等价于辛LCD码，确定辛自正交码的可达核维数并关联图匹配给出码构造。
Both MDS and Euclidean self-dual codes have theoretical and practical importance and the study of MDS self-dual codes has attracted lots of attention in recent years. In particular, determining existence of $q$-ary MDS self-dual codes for various lengths has been investigated extensively. The problem is completely solved for the case where $q$ is even. The current paper focuses on the case where $q$ is odd. We construct a few classes of new MDS self-dual code through generalized Reed-Solomon codes. More precisely, we show that for any given even length $n$ we have a $q$-ary MDS code as long as…
Linear codes with complementary duals (LCD) have a great deal of significance amongst linear codes. Maximum distance separable (MDS) codes are also an important class of linear codes since they achieve the greatest error correcting and detecting capabilities for fixed length and dimension. The construction of linear codes that are both LCD and MDS is a hard task in coding theory. In this paper, we study the constructions of LCD codes that are MDS from negacyclic codes over finite fields of odd prime power $q$ elements. We construct four families of MDS negacyclic LCD codes of length $n|\frac{q…
In this paper, we explore some properties of Galois hulls of cyclic serial codes over a chain ring and we devise an algorithm for computing all the possible parameters of the Euclidean hulls of that codes. We also establish the average $p^r$-dimension of the Euclidean hull, where $\mathbb{F}_{p^r}$ is the residue field of $R$, and we provide some results of its relative growth.
Hulls and sums of separable constacyclic codes over $\mathbb{F}_q \times (\mathbb{F}_q+v\mathbb{F}_q)$ and new quantum codes
研究在环F_q×(F_q+vF_q)上可分常循环码的对偶、壳与和的生成多项式，利用其格雷像，提出两种构造量子纠错码的方法，生成了参数更优的新量子码。
Two variants of Twisted Reed-Solomon Codes
本文研究两类扭曲里德-所罗门码变体，给出其为MDS码的充要条件，并通过更大的Schur平方维数构造出不等价于RS码的新MDS码，为量子码构造奠定基础。
This paper studies the theory of linear analog error correction coding. Since classical concepts of minimum Hamming distance and minimum Euclidean distance fail in the analog context, a new metric, termed the "minimum (squared Euclidean) distance ratio," is defined. It is shown that linear analog codes that achieve the largest possible value of minimum distance ratio also achieve the smallest possible mean square error (MSE). Based on this achievability, a concept of "maximum distance ratio expansible (MDRE)" is established, in a spirit similar to maximum distance separable (MDS). Existing cod…
The hulls of linear and cyclic codes have been extensively studied due to their wide applications. In this paper, the average dimension of the Hermitian hull of constacyclic codes of length $n$ over a finite field $\mathbb{F}_{q^2}$ is determined together with some upper and lower bounds. It turns out that either the average dimension of the Hermitian hull of constacyclic codes of length $n$ over $\mathbb{F}_{q^2}$ is zero or it grows the same rate as $n$. Comparison to the average dimension of the Euclidean hull of cyclic codes is discussed as well.
Non-GRS type Euclidean and Hermitian LCD codes and Their Applications for EAQECCs
本文基于非GRS类型的线性码构造了欧几里得LCD码、赫尔米特LCD码及小维度包络码，并给出了相关上界，同时应用这些码构造了EAQECCs，并证明了GRL码在k>ℓ时非GRS。
Linear Codes with Certain Dimension of Hermitian Hulls
本文研究了Hermite $\ell$-互补码的计数性质和渐进行为，发现其与无限制码在渐近重量分布上存在相似性，并证明了当字母表大小趋于无穷大时，Hermite自正交码类中的MDS码在渐进行为上是渐近密集的。
Algebraic methods for the design of series of maximum distance separable (MDS) linear block and convolutional codes to required specifications and types are presented. Algorithms are given to design codes to required rate and required error-correcting capability and required types. Infinite series of block codes with rate approaching a given rational $R$ with $0<R<1$ and relative distance over length approaching $(1-R)$ are designed. These can be designed over fields of given characteristic $p$ or over fields of prime order and can be specified to be of a particular type such as (i) dual-conta…
A note on the hull and linear complementary pair of cyclic codes
本文利用基本对偶零点与迹表示刻画有限域上长度 $q^m-1$ 的循环码的 LCD 性质和 LCP，并给出任意长度循环码包络维数及两码交集维数公式。
The hull $H(C)$ of a linear code $C$ is defined by $H(C)=C \cap C^\perp$. A linear code with a complementary dual (LCD) is a linear code with $H(C)=\{0\}$. The dimension of the hull of a code is an invariant under permutation equivalence. For binary and ternary codes the dimension of the hull is also invariant under monomial equivalence and we show that this invariant is determined by the extended weight enumerator of the code.\\ The hull of a code is not invariant under monomial equivalence if $q\geq 4$. We show that every ${\mathbb F}_q $-linear code is monomial equivalent with an LCD code i…
In this paper, we give a method for constructing linear codes with small hulls by generalizing the method in \cite{LCD-T-matric}. As a result, we obtain many optimal Euclidean LCD codes and Hermitian LCD codes, which improve the previously known lower bound on the largest minimum distance. We also obtain many optimal codes with one-dimension hull. Furthermore, we give three tables about formally self-dual LCD codes.
In this paper, we propose two novel modulation concepts based on a simple maximum distance separable (MDS) code { and show that these concepts can achieve better error performance than index modulation (IM) and related schemes.} In the first concept, we use amplitude and phase levels to form a simple MDS code, whereas, in the second one, in-phase and quadrature components of codeword elements are used to construct the MDS code. We depict practical schemes for using the proposed concepts with orthogonal frequency division multiplexing (OFDM). We analyze the performance in terms of the minimum E…
A linear code is called an MDS self-dual code if it is both an MDS code and a self-dual code with respect to the Euclidean inner product. The parameters of such codes are completely determined by the code length. In this paper, we consider new constructions of MDS self-dual codes via generalized Reed-Solomon (GRS) codes and their extended codes. The critical idea of our constructions is to choose suitable evaluation points such that the corresponding (extended) GRS codes are self-dual. The evaluation set of our constructions is consists of a subgroup of finite fields and its cosets in a bigger…
Shortest Embeddings of Linear Codes with Arbitrary Hull Dimension
本文研究了线性码在欧几里得和海利特情况下的任意围维度最短嵌入，通过二次型理论和经典群论工具确定其精确长度，并改进了An等人结果，提出了分类和构造算法，获得了与BKLC数据库不等价的最优码。
For a prime power $q$, an integer $m$ and $0\leq e\leq m-1$ we study the $e$-Galois hull dimension of Gabidulin codes $G_k(\boldsymbolα)$ of length $m$ and dimension $k$ over $\mathbb{F}_{q^m}$. Using a self-dual basis $\boldsymbolα$ of $\mathbb{F}_{q^m}$ over $\mathbb{F}_q$, we first explicitly compute the hull dimension of $G_k(\boldsymbolα)$. Then a necessary and sufficient condition of $G_k(\boldsymbolα)$ to be linear complementary dual (LCD), self-orthogonal and self-dual will be provided. We prove the existence of $e$-Galois (where $e=\frac{m}{2}$) self-dual Gabidulin codes of length $m$…
Entanglement-assisted quantum (QUENTA) codes are a subclass of quantum error-correcting codes which use entanglement as a resource. These codes can provide error correction capability higher than the codes derived from the traditional stabilizer formalism. In this paper, it is shown a general method to construct QUENTA codes from cyclic codes. Afterwards, the method is applied to Reed-Solomon codes, BCH codes, and general cyclic codes. We use the Euclidean and Hermitian construction of QUENTA codes. Two families of QUENTA codes are maximal distance separable (MDS), and one is almost MDS or alm…
Hermitian Self-dual Generalized Reed-Solomon Codes
本文研究了埃尔米特自对偶广义里德-所罗门码的构造与存在性，证明了当n≤q+1时仅存在两类此类码，并提出两种显式构造方法。
On Galois self-orthogonal algebraic geometry codes
本文研究伽罗瓦自正交代数几何码，提出判别准则，并从射影直线、椭圆曲线、超椭圆曲线和厄米特曲线构造多类新的 MDS 及非 MDS 伽罗瓦自正交代数几何码，同时给出嵌入方法以扩展构造。
Decoding Algorithms for Twisted GRS Codes
本文提出基于高斯消元法的扭曲广义RS码译码算法，可纠正MDS码最多$\floor{\frac{n-k}{2}}$个错误，复杂度$O(n^3)$，并适用于近MDS码。
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。