The study of ℤpℤp[u, v]-additive cyclic codes and their application in obtaining Optimal and MDSS codes

Abstract

Let S = ℤp[u, v]/〈u2, v2, uv − uv〉 be a semi-local ring, where p is a prime number. In the present article, we determine the generating sets of S and use them to construct the structures of ℤpS-additive cyclic and constacyclic codes. The minimal polynomials and spanning sets of ℤpS-additive cyclic and constacyclic codes are also determined. These codes are identified as S[y]-submodules of the ring Sβ1, β2 = ℤp[y]/〈yβ1 − 1〉 × S[y]/〈yβ2 − 1〉. Some results that represent the relationship between the minimal polynomials of ℤpS-additive cyclic codes and their duals have been obtained. Furthermore, optimal ℤpS-additive codes and maximum distance separable codes have been evaluated (see Table 1). Finally, we use MAGMA software to find the parameters of Optimal and MDSS codes.

Keywords

• polynomial ring
• additive cyclic codes
• gray map
• 94b05
• 94b15
• 94b60