Repeated root cyclic codes over ℤp2+uℤp2 and their Lee distances

Abstract

In this paper we have studied repeated root cyclic codes of length pk over R=ℤp2+uℤp2, u2 = 0, where p is a prime and k is a positive integer. We have determined a unique set of generators for these codes and obtained some results on their Lee distances. A minimal spanning set for them has been obtained and their ranks are determined. Further, we have determined the complete algebraic structure of principally generated cyclic codes in this class. An upper bound for the Lee distance of linear codes over R is presented. We have considered two Gray maps ψ:R→ℤp4 and ϕ1:R→ℤp22, and using them, we have obtained some optimal binary linear codes as well as some quaternary linear codes from cyclic codes of length 4 over ℤ4+ uℤ4. Three of the quaternary linear codes obtained are new, and the remaining of them have the best known parameters for their lengths and types. We have also obtained some optimal ternary codes of length 12 as Gray images of repeated root cyclic codes of length 3 over ℤ9+ uℤ9. © 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.