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, cilt.29, sa.4, ss.303-312, 2018 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 29 Sayı: 4
  • Basım Tarihi: 2018
  • Doi Numarası: 10.1007/s00200-017-0343-x
  • Dergi Adı: APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.303-312
  • Anahtar Kelimeler: Quasi-cyclic codes, Self-dual codes, Cubic construction, BINARY-CODES
  • Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

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.