REPEATED-ROOT CONSTACYCLIC CODES OF LENGTH 2ps OVER GALOIS RINGS

In this paper, we consider the structure of gamma-constacyclic codes of length 2p(s) over the Galois ring GR(p(a), m) for any unit gamma of the form xi(0) + p xi(1) + p(2)z, where z is an element of GR(p(a), m) and xi(0), xi(1) are nonzero elements of the set tau(p, m). Here tau(p, m) denotes a complete set of representatives of the cosets GR(p(a),m)/pGR(p(a),m) = F(p)m in GR(p(a),m). When gamma is not a square, the rings Rp (a, m, gamma) = Gr(p(a),m)[x]/< x(2ps) -gamma > is a chain ring with maximal ideal < x(2) - delta >, where delta p(s) = xi 0, and the number of codewords of gamma-constacyclic code are provided. Furthermore, the self-orthogonal and self-dual gamma-constacyclic codes of length 2p(s) over GR(p(a), m) are also established. Finally, we determine the Rosenbloom-Tsfasman (RT) distances and weight distributions of all such codes.