ADDITIVE TOEPLITZ CODES OVER F-4

ŞAHİN M., Ozimamoglu H.

ADVANCES IN MATHEMATICS OF COMMUNICATIONS, cilt.14, sa.2, ss.379-395, 2020 (SCI-Expanded, Scopus) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 14 Sayı: 2
  • Basım Tarihi: 2020
  • Doi Numarası: 10.3934/amc.2020026
  • Dergi Adı: ADVANCES IN MATHEMATICS OF COMMUNICATIONS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Applied Science & Technology Source, MathSciNet, zbMATH
  • Sayfa Sayıları: ss.379-395
  • Anahtar Kelimeler: Additive codes, additive circulant codes, codes over F-4, optimal codes, classification, SELF-DUAL CODES
  • Ankara Üniversitesi Adresli: Evet

Özet

In this paper, we introduce additive Toeplitz codes over F-4. The additive Toeplitz codes are a generalization of additive circulant codes over F-4. We find many optimal additive Toeplitz codes (OATC) over F-4. These optimal codes also contain optimal non-circulant codes, so we find new additive codes in this manner. We provide some theorems to partially classify OATC. Then, we give a new algorithm that fully classifies OATC by combining these theorems with Gaborit's algorithm. We classify OATC over F-4 of length up to 13. We obtain 2 inequivalent optimal additive toeplitz codes (IOATC) that are noncirculant codes of length 5, 92 of length 8, 2068 of length 9, and 39 of length 11. Moreover, we improve an idea related to quadratic residue codes to construct optimal and near-optimal additive Toeplitz codes over F-4 of length prime p. We obtain many optimal and near-optimal additive Toeplitz codes for some primes p from this construction.