On integral weight spectra of the MDS codes cosets of weight 1, 2, and 3

On the weight distribution of the cosets of MDS codes

The weight distribution of the cosets of maximum distance separable (MDS) codes is considered. In 1990, P.G. Bonneau proposed a relation to obtain the full weight distribution of a coset of an MDS code with minimum distance $d$ using the known numbers of vectors of weights $\le d-2$ in this coset. In this paper, the Bonneau formula is transformed into a more structured and convenient form. The new version of the formula allows to consider effectively cosets of distinct weights $W$. (The weight $W$ of a coset is the smallest Hamming weight of any vector in the coset.) For each of the considered…

Construction of MDS Euclidean Self-Dual Codes via Two Subsets

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…

Entanglement-assisted quantum MDS codes constructed from constacyclic codes

Recently, entanglement-assisted quantum error correcting codes (EAQECCs) have been constructed by cyclic codes and negacyclic codes. In this paper, by analyzing the cyclotomic cosets in the defining set of constacyclic codes, we constructed three classes of new EAQECCs which satisfy the entanglement-assisted quantum Singleton bound. Besides, three classes of EAQECCs with maximal entanglement from constacyclic codes are constructed in the meanwhile.

两类具有大最小距离的量子MDS码

Two Classes of Quantum MDS Codes with Large Minimal Distance

本文利用有限域乘法结构和陪集选择，构造了两类参数全新的量子MDS码，部分码的最小距离超过q/2。

通过多个子集构造MDS欧氏自对偶码

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%。

加里默型界限用于有限域上的加法码，积分和分数MDS码

Griesmer type bounds for additive codes over finite fields, integral and fractional MDS codes

本文研究了有限域上加法码的加里默型界限，探讨了积分和分数MDS码的性质及分类方法。