New cubic self-dual codes of length 54, 60 and 66
APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING, vol.29, no.4, pp.303-312, 2018 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 29 Issue: 4
- Publication Date: 2018
- Doi Number: 10.1007/s00200-017-0343-x
- Journal Name: APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Page Numbers: pp.303-312
- Keywords: Quasi-cyclic codes, Self-dual codes, Cubic construction, BINARY-CODES
- Open Archive Collection: AVESIS Open Access Collection
- Middle East Technical University Affiliated: Yes
Abstract
We study the construction of quasi-cyclic self-dual codes, especially of binary cubic ones. We consider the binary quasi-cyclic codes of length with the algebraic approach of Ling and Sol, (IEEE Trans Inf Theory 47(7):2751-2760, 2001. doi:. In particular, we improve the previous results by constructing 1 new binary [54, 27, 10], 6 new [60, 30, 12] and 50 new [66, 33, 12] cubic self-dual codes. We conjecture that there exist no more binary cubic self-dual codes with length 54, 60 and 66.