Self-dual codes over F-2 x (F-2 + vF(2))
CRYPTOGRAPHY AND COMMUNICATIONS-DISCRETE-STRUCTURES BOOLEAN FUNCTIONS AND SEQUENCES, vol.13, no.1, pp.129-141, 2021 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 13 Issue: 1
- Publication Date: 2021
- Doi Number: 10.1007/s12095-020-00461-z
- Journal Name: CRYPTOGRAPHY AND COMMUNICATIONS-DISCRETE-STRUCTURES BOOLEAN FUNCTIONS AND SEQUENCES
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Compendex, INSPEC, zbMATH
- Page Numbers: pp.129-141
- Keywords: Codes over direct product rings, Minimum distance, Self-dual codes, Generator matrix
- Istanbul University Affiliated: Yes
Abstract
In this study we consider Euclidean and Hermitian self-dual codes over the direct product ring F-2 x (F-2 + vF(2)) where v(2) = v. We obtain some theoretical outcomes about self-dual codes via the generator matrices of free linear codes over F-2 x(F-2 + vF(2)). Also, we obtain upper bounds on the minimum distance of linear codes for both the Lee distance and the Gray distance. Moreover, we find some free Euclidean and free Hermitian self-dual codes over F-2 x (F-2 + vF(2)) via some useful construction methods.