New cubic self-dual codes of length 54, 60 and 66


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Comak P. , Kim J. L. , Ozbudak F.

APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING, vol.29, no.4, pp.303-312, 2018 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 29 Issue: 4
  • Publication Date: 2018
  • Doi Number: 10.1007/s00200-017-0343-x
  • Title of Journal : APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING
  • Page Numbers: pp.303-312

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.