REPEATED-ROOT CYCLIC AND NEGACYCLIC CODES OF PRIME POWER LENGTHS WITH A FINITE COMMUTATIVE CHAIN RING ALPHABET

Abstract

We dicuss foundational and theoretical aspects of algebraic coding theory with the concentration on repeated-root cyclic and negacyclic codes of prime power length ps over a finite commutative chain ring R. Among other things, the nilpotency indeces of x−1 andx+1inthe ambient rings R[x] xps−1 and R[x] xps +1, respectively, are established