A Unified Approach to Construct MDS Self-Dual Codes via Reed-Solomon Codes
A Unified Approach to Construct MDS Self-Dual Codes via Reed-Solomon Codes
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DOI：
10.1109/tit.2020.2963975
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发表时间：
2020-01
影响因子：
2.5
通讯作者：
Aixian Zhang;K. Feng
中科院分区：
文献类型：
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作者：
Aixian Zhang;K. Feng
MDS码和自对偶码是编码理论中重要的经典码族。因此，对MDS自对偶码的研究具有重要的意义。完全解决了有限域${\mathbb F}_{q}$上MDS自对偶码的存在性，且$q$为偶。在文献中，有许多已知的元q元为奇数的MDS自对偶码结构。本文给出了一个关于MDS自对偶码存在性的统一方法，给出了简明的表述和简化的证明。说明了一些已知的结果也可以在这个框架中表述。此外，我们还得到了一些新的MDS自对偶码，特别是对于$q$不是平方的情况。
MDS codes and self-dual codes are important families of classical codes in coding theory. Therefore, it is of interest to investigate MDS self-dual codes. The existence of MDS self-dual codes over finite field ${\mathbb F}_{q}$ is competely solved for $q$ is even. In the literature, there are many known constructions of MDS self-dual codes for $q$ is odd. In this paper, we present a unified approach on the existence of MDS self-dual codes with concise statements and simplified proof. It is illustrated that some of known results can also be stated in this framework. Furthermore, we can obtain some new MDS self-dual codes, especially for the case when $q$ is not a square.