Search

Let p ≠ 3 be any prime. The algebraic structures of all λ -constacyclic codes of length 3 p s over the finite commutative chain ring R = F p m + u F p m are provided by classifying all ideals of the local ring R [ x ] 〈 x 3 p s − λ 〉. Using these structures, in this paper, the exact values of Hamming distances of all such λ -constacyclic codes of length 3 p s are established. As an application, we identify all maximal distance separable λ -constacyclic codes of length 3 p s. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, the explicit expressions for the generating idempotents, check polynomials and the parameters of all minimal cyclic codes of length over are obtained, where is an odd prime different from the characteristic of , and are positive integers with , and . Our results generalize the main results in Pruthi and Arora (1997) and Arora and Pruthi (1999), which considered the cases and respectively. We propose an approach different from those in Pruthi and Arora (1997) and Arora and Pruthi (1999) to obtain the generating idempotents. [Copyright &y& Elsevier]