On a Class of Constacyclic Codes of Length 4 p s over F p m [ u ] (u a)

Abstract

© 2019 Academy of Mathematics and Systems Science, Chinese Academy of Sciences. For any odd prime p such that pm 3 (mod 4), consider all units of the finite commutative chain ring Ra = F pm[u]ua = Fpm + uFpm + ua1Fpm that have the form = 0 + u1 + ua1a1, where 0;1; a1 Fpm, 0 = 0; 1 = 0. The class of -constacyclic codes of length 4ps over Ra is investigated. If the unit is a square, each -constacyclic code of length 4ps is expressed as a direct sum of a - constacyclic code and a -constacyclic code of length 2ps. In the main case that the unit is not a square, we prove that the polynomial x4 0 can be decomposed as a product of two quadratic irreducible and monic coprime factors, where ps 0 = 0. From this, the ambient ring Ra[x] x4ps is proven to be a principal ideal ring, whose maximal ideals are x2 +x+22 and x2 2x+22, where 0 = 44: We also give the unique self-dual Type 1 -constacyclic codes of length 4ps over Ra. Furthermore, conditions for a Type 1 -constacyclic code to be self-orthogonal and dual-containing are provided.