Symbol-Pair Distances of Repeated-Root Negacyclic Codes of Length 2s over Galois Rings

Negacyclic codes of length 2(s) over the Galois ring GR(2(a), m) are linearly ordered under set-theoretic inclusion, i.e., they are the ideals <(x + 1)(i)>, 0 <= i <= 2(s) a, of the chain ring GR(2(a), m)[x]/< x(2s) + 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 F-2m (i.e., a = 1), the symbol-pair distance distribution of constacyclic codes over F-2m verifies the Singleton bound for such symbol-pair codes, and provides all maximum distance separable symbol-pair constacyclic codes of length 2(s) over F-2m.