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

DOI10.1109/TIT.2022.3163813arXiv2106.07840MaRDI QIDQ6370324

Qi Wang, Chun-Ming Tang, Cunsheng Ding

Publication date: 14 June 2021

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 $1lequleq{2}^{m-1}$, which are cyclic, reversible and BCH codes over $mathrmGF(2^m)$. 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.

Mathematics Subject Classification ID

Linear codes (general theory) (94B05) Cyclic codes (94B15)

This page was built for publication: The subfield codes and subfield subcodes of a family of MDS codes

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6370324)