On Symbol-Triple Distance of a Class of Constacyclic Codes of Length 3p^s Over F _p^m + uF _p^m

Abstract

Let p = 3 be any prime. In this paper, we completely determine symbol-triple distance of all γ-constacyclic codes of length 3p s over the finite commutative chain ring R = F p m + uF p m , where γ is a unit of R which is not a cube in F p m . We give the necessary and sufficient condition for a symbol-triple γ-constacyclic code to be an MDS symbol-triple code. Using that, we establish all MDS symbol-triple γconstacyclic codes of length 3p s over R. Some examples of the symbol-triple distance of γ-constacyclic codes of length 3p s over R are provided. We also list some new MDS symbol-triple γ-constacyclic codes of length 3p s over R, where γ is not a cube in F p m . INDEX TERMS Constacyclic codes, dual codes, chain rings, MDS symbol-triple codes, symbol-triple codes.