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A Unified Approach to Construct MDS Self-Dual Codes via Reed-Solomon Codes.
- Source :
- IEEE Transactions on Information Theory; Jun2020, Vol. 66 Issue 6, p3650-3656, 7p
- Publication Year :
- 2020
-
Abstract
- 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. [ABSTRACT FROM AUTHOR]
- Subjects :
- REED-Solomon codes
BINARY codes
FINITE fields
CODING theory
LINEAR codes
SQUARE
Subjects
Details
- Language :
- English
- ISSN :
- 00189448
- Volume :
- 66
- Issue :
- 6
- Database :
- Complementary Index
- Journal :
- IEEE Transactions on Information Theory
- Publication Type :
- Academic Journal
- Accession number :
- 143457077
- Full Text :
- https://doi.org/10.1109/TIT.2020.2963975