On double cyclic codes over Z2 + uZ2


AIMS Mathematics, vol.9, no.5, pp.11076-11091, 2024 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 9 Issue: 5
  • Publication Date: 2024
  • Doi Number: 10.3934/math.2024543
  • Journal Name: AIMS Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Directory of Open Access Journals
  • Page Numbers: pp.11076-11091
  • Keywords: double cyclic codes, optimal codes, self-dual cyclic codes, Z2 + uZ2
  • Yıldız Technical University Affiliated: Yes


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.