Constacyclic codes of length np^sover F<inf>p</inf>m + uF<inf>p</inf>m

Abstract

© 2018 AIMS. Let Fpm be a finite field of cardinality pmand R = Fpm [u]/〈u2〉 = Fpm + uFpm (u2= 0), where p is a prime and m is a positive integer. For any λ ∈ F×pm, an explicit representation for all distinct λ-constacyclic codes over R of length npsis given by a canonical form decomposition for each code, where s and n are arbitrary positive integers satisfying gcd(p, n) = 1. For any such code, using its canonical form decomposition the representation for the dual code of the code is provided. Moreover, representations for all distinct cyclic codes, negacyclic codes and their dual codes of length npsover R are obtained, and self-duality for these codes are determined. Finally, all distinct self-dual negacyclic codes over F5+ uF5of length 2 · 3t· 5sare listed for any positive integer t.