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arXiv · 2106.07840

The subfield codes and subfield subcodes of a family of MDS codes

Chunming Tang·Qi Wang·Cunsheng Ding
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Abstract

Maximum distance separable (MDS) codes are very important in both theory and practice. There is a classical construction of a family of $[2^m+1, 2u-1, 2^m-2u+3]$ MDS codes for $1 \leq u \leq 2^{m-1}$, which are cyclic, reversible and BCH codes over $\mathrm{GF}(2^m)$. The objective of this paper is to study the quaternary subfield subcodes and quaternary subfield codes of a subfamily of the MDS codes for even $m$. A family of quaternary cyclic codes is obtained. These quaternary codes are distance-optimal in some cases and very good in general. Furthermore, infinite families of $3$-designs from these quaternary codes are presented.

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Chunming Tang, Qi Wang, Cunsheng Ding. 2021-06-15. The subfield codes and subfield subcodes of a family of MDS codes. https://arxiv.org/abs/2106.07840

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