Some optimal entanglement-assisted quantum codes constructed from quaternary Hermitian linear complementary dual codes

一种构造四元 Hermitian 自对偶码的方法及其在量子码中的应用

A method for constructing quaternary Hermitian self-dual codes and an application to quantum codes

本文提出四元修正四 μ-循环 Hermitian 自对偶码的构造方法，首次得到两个 [56,28,16] 码，改进已知下界并导出量子 [[56,0,16]] 码。

Some restrictions on the weight enumerators of near-extremal ternary self-dual codes and quaternary Hermitian self-dual codes

We give restrictions on the weight enumerators of ternary near-extremal self-dual codes of length divisible by $12$ and quaternary near-extremal Hermitian self-dual codes of length divisible by $6$. We consider the weight enumerators for which there is a ternary near-extremal self-dual code of length $12m$ for $m =3,4,5,6$. Also we consider the weight enumerators for which there is a quaternary near-extremal Hermitian self-dual code of length $6m$ for $m =4,5,6$.

Construction of quaternary Hermitian LCD codes

We introduce a general construction of many Hermitian LCD $[n, k]$ codes from a given Hermitian LCD $[n, k]$ code. Furthermore, we present some results on punctured codes and shortened codes of quaternary Hermitian LCD codes. As an application, we improve some of the previously known lower bounds on the largest minimum weights of quaternary Hermitian LCD codes of length $12 \le n \le 30$.

Quaternary Hermitian self-dual codes of lengths 26, 32, 36, 38 and 40 from modifications of well-known circulant constructions

In this work, we give three new techniques for constructing Hermitian self-dual codes over commutative Frobenius rings with a non-trivial involutory automorphism using $λ$-circulant matrices. The new constructions are derived as modifications of various well-known circulant constructions of self-dual codes. Applying these constructions together with the building-up construction, we construct many new best known quaternary Hermitian self-dual codes of lengths 26, 32, 36, 38 and 40.

Remark on subcodes of linear complementary dual codes

We show that any ternary Euclidean (resp.\ quaternary Hermitian) linear complementary dual $[n,k]$ code contains a Euclidean (resp.\ Hermitian) linear complementary dual $[n,k-1]$ subcode for $2 \le k \le n$. As a consequence, we derive a bound on the largest minimum weights among ternary Euclidean linear complementary dual codes and quaternary Hermitian linear complementary dual codes.

Classification of generalized Hadamard matrices H(6,3) and quaternary Hermitian self-dual codes of length 18

All generalized Hadamard matrices of order 18 over a group of order 3, H(6,3), are enumerated in two different ways: once, as class regular symmetric (6,3)-nets, or symmetric transversal designs on 54 points and 54 blocks with a group of order 3 acting semi-regularly on points and blocks, and secondly, as collections of full weight vectors in quaternary Hermitian self-dual codes of length 18. The second enumeration is based on the classification of Hermitian self-dual [18,9] codes over GF(4), completed in this paper. It is shown that up to monomial equivalence, there are 85 generalized Hadamar…

线性码关于Hermitian和辛对偶维数的比较单调性

Comparative monotonicity of linear codes by Hermitian and symplectic hull dimensions

本文通过推导Hermitian和辛对偶维数的闭式比率分解，比较了两种对偶维数下线性码数量的渐近行为，并利用Witt分类解释了差异，进而转化为纠缠辅助量子码数量的单调性陈述。

由2-(47,23,11)设计导出的长度为48的自对偶近极值三元码的新例子

New examples of self-dual near-extremal ternary codes of length 48 derived from 2-(47,23,11) designs

针对长度48的自对偶近极值三元码在$A_{12}$其他取值下的存在性问题，利用带6阶自同构群的对称2-(47,23,11)设计，构造出150个新$A_{12}$取值的该类码，拓展了已知实例范围。