Optimal binary codes derived from F2F4-additive cyclic codes

Abualrub T., Aydin N., Aydoğdu İ.

JOURNAL OF APPLIED MATHEMATICS AND COMPUTING, vol.64, pp.71-87, 2020 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 64
  • Publication Date: 2020
  • Doi Number: 10.1007/s12190-020-01344-5
  • Journal Name: JOURNAL OF APPLIED MATHEMATICS AND COMPUTING
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, ABI/INFORM, Aerospace Database, Communication Abstracts, Compendex, INSPEC, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Page Numbers: pp.71-87
  • Keywords: F2F4-additive cyclic codes, Duality, Quantum codes, Optimal codes
  • Yıldız Technical University Affiliated: Yes

Abstract

In this paper, we study the algebraic structure of additive cyclic codes over the alphabet Fr 2 x Fs 4 = Fr 2Fs 4, where r and s are non-negative integers, F2 = GF(2) and F4 = GF(4) are the finite fields of 2 and 4 elements, respectively. We determine generator polynomials for F2F4-additive cyclic codes. We also introduce a linear map W that depends on the trace map T to relate these codes to binary linear codes over F2. Further, we investigate the duals of F2F4-additive cyclic codes. We show that the dual of any F2F4-additive cyclic code is another F2F4-additive cyclic code. Using the mapping W, we provide examples of F2F4-additive cyclic codes whose binary images have optimal parameters. We also consider additive cyclic codes over F4 and give some examples of optimal parameter quantum codes over F4.