On double cyclic codes over Z2 + uZ2

AYDOĞDU İ.

AIMS Mathematics, cilt.9, sa.5, ss.11076-11091, 2024 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 9 Sayı: 5
  • Basım Tarihi: 2024
  • Doi Numarası: 10.3934/math.2024543
  • Dergi Adı: AIMS Mathematics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Directory of Open Access Journals
  • Sayfa Sayıları: ss.11076-11091
  • Anahtar Kelimeler: double cyclic codes, optimal codes, self-dual cyclic codes, Z2 + uZ2
  • Yıldız Teknik Üniversitesi Adresli: Evet

Özet

In this paper, we introduced double cyclic codes over Rr × Rs, where R = ℤ2 + uℤ2 = {0, 1, u, 1 + u} is the ring with four elements and u2 = 0. We first determined the generator polynomials of R-double cyclic codes for odd integers r and s, then gave the generators of duals of free double cyclic codes over Rr × Rs. By defining a linear Gray map, we looked at the binary images of R-double cyclic codes and gave several examples of optimal parameter binary linear codes obtained from R-double cyclic codes. Moreover, we studied self-dual R-double cyclic codes and presented an example of a self-dual R-double cyclic code.