Cyclic and negacyclic codes of length 4 p^sover F<inf>p</inf>^m+ u F<inf>pm</inf>

Abstract

© 2018 World Scientific Publishing Company. Let Fpmbe the finite field of order pm, where pmis an odd prime and m is a positive integer. In this paper, we determine the algebraic structures of all cyclic and negacyclic codes of length 4psover the finite commutative chain ring R = Fpm+ uFpm, where u2= 0 and s is a positive integer. We also obtain the number of codewords in each of these codes. Among others, we establish the duals of all such codes and derive some self-dual cyclic and negacyclic codes of length 4psover R.