Symbol-pair distances of repeated-root negacyclic codes of length 2^sover Galois rings

Abstract

Negacyclic codes of length 2s over the Galois ring GR(2a, m) are linearly ordered under set-theoretic inclusion, i.e., they are the ideals <(x+1)i>, 0≤ i≤ 2sa, of the chain ring GR(2aaa, m) [x ]/< x2s +1>. This structure is used to obtain the symbol-pair distances of all such negacyclic codes. Among others, for the special case when the alphabet is the finite field F2m (i.e., a=1), the symbol-pair distance distribution of constacyclic codes over F2m verifies the Singleton bound for such symbol-pair codes, and provides all maximum distance separable symbol-pair constacyclic codes of length 2s over F2m.