The subfield codes and subfield subcodes of a family of MDS codes
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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 ≤ u ≤ 2^m-1, which are cyclic, reversible and BCH codes over 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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