Reversible Gk -codes with applications to DNA codes

Korban A., Şahinkaya S., Ustun D.

Designs, Codes, and Cryptography, cilt.90, sa.7, ss.1679-1694, 2022 (SCI-Expanded, Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 90 Sayı: 7
  • Basım Tarihi: 2022
  • Doi Numarası: 10.1007/s10623-022-01067-7
  • Dergi Adı: Designs, Codes, and Cryptography
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, PASCAL, Applied Science & Technology Source, Compendex, Computer & Applied Sciences, INSPEC, MathSciNet, zbMATH
  • Sayfa Sayıları: ss.1679-1694
  • Anahtar Kelimeler: DNA codes, Group matrix rings, Reversible Gk-codes
  • Ankara Üniversitesi Adresli: Hayır

Özet

In this paper, we give a matrix construction method for designing DNA codes that come from group matrix rings. We show that with our construction one can obtain reversible Gk-codes of length kn, where k, n∈ N, over the finite commutative Frobenius ring R. We employ our construction method to obtain many DNA codes over F4 that satisfy the Hamming distance, the reverse, the reverse-complement and the fixed GC-content constraints. Moreover, we improve many lower bounds on the sizes of some known DNA codes and we also give new lower bounds on the sizes of DNA codes of lengths 48, 56, 60, 64 and 72 for some fixed values of the Hamming distance d.