On the Symbol-Pair Distance of Repeated-Root Constacyclic Codes of Prime Power Lengths

Let p be a prime, and λ be a nonzero element of the finite field F _p^m . The λ-constacyclic codes of length p ^s over F _p^m are linearly ordered under set-theoretic inclusion, i.e., they are the ideals 〈(x - λ ₀ ) ⁱ 〉, 0 ≤ i ≤ p ^s of the chain ring [(F _p^m [x])/((x ^{p s} - λ))]. This structure is used to establish the symbol-pair distances of all such λ-constacyclic codes. Among others, all maximum distance separable symbol-pair constacyclic codes of length ps are obtained.