Construction of MDS Euclidean Self-Dual Codes via Two Subsets
Construction of MDS Euclidean Self-Dual Codes via Two Subsets
复制标题
通过两个子集构造MDS欧几里得自对偶码
DOI：
10.1109/tit.2021.3085768
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发表时间：
2020-05
期刊：
影响因子：
--
通讯作者：
Fang-Wei Fu
中科院分区：
文献类型：
--
作者：
Weijun Fang;Shu-Tao Xia;Fang-Wei Fu
一元元MDS欧几里得自对偶码的参数完全由其长度决定，构造具有新长度的MDS欧几里得自对偶码近年来得到了广泛的研究。本文进一步研究了利用广义Reed-Solomon码及其扩展码构造MDS欧几里得自对偶码的方法。我们的主要思想是选择合适的评价点，使相应的（扩展的）GRS码是欧几里得自对偶的。首先，我们考虑评价集由两个不相交的子集组成，其中一个子集基于迹函数，另一个子集是子空间及其余集的并集。然后构造了四个新的MDS欧几里得自对偶码族。其次，我们给出了一个简单而有用的引理，以保证有限域的两个相交子集的对称差可以作为期望的求值集。基于这一引理，我们推广了第一个构造，并给出了两个新的MDS欧几里得自对偶码族。最后，利用两个具有非空交的乘子群及其余集，给出了具有柔性参数的MDS欧几里得自对偶码的三种一般构造。明确构造了几个新的MDS欧几里得自对偶码族。
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 of which is based on the trace function, the other one is a union of a subspace and its cosets. Then four new families of MDS Euclidean self-dual codes are constructed. Secondly, we give a simple but useful lemma to ensure that the symmetric difference of two intersecting subsets of finite fields can be taken as the desired evaluation set. Based on this lemma, we generalize our first construction and provide two new families of MDS Euclidean self-dual codes. Finally, by using two multiplicative subgroups and their cosets which have nonempty intersection, we present three generic constructions of MDS Euclidean self-dual codes with flexible parameters. Several new families of MDS Euclidean self-dual codes are explicitly constructed.
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DOI：
10.1109/isit.2004.1365563
发表时间：
2004-06
期刊：
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影响因子：
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作者：
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通讯作者：
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DOI：
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期刊：
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期刊：
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发表时间：
2015-02
期刊：
Designs, Codes and Cryptography
影响因子：
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作者：
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通讯作者：
Yiansheng Yang;W. Cai
影响因子：
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