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−1andx+1inthe
 ambient rings R[x]
 xps−1
 and R[x]
 xps+1
 , respectively, are established.