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The Subfield Codes and Subfield Subcodes of a Family of MDS Codes.
- Source :
-
IEEE Transactions on Information Theory . Sep2022, Vol. 68 Issue 9, p5792-5801. 10p. - Publication Year :
- 2022
-
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, two infinite families of 3-designs from these quaternary codes and their duals are presented. [ABSTRACT FROM AUTHOR]
- Subjects :
- *CYCLIC codes
*LIQUID crystal displays
*LINEAR codes
Subjects
Details
- Language :
- English
- ISSN :
- 00189448
- Volume :
- 68
- Issue :
- 9
- Database :
- Academic Search Index
- Journal :
- IEEE Transactions on Information Theory
- Publication Type :
- Academic Journal
- Accession number :
- 158603974
- Full Text :
- https://doi.org/10.1109/TIT.2022.3163813