On the Symbol-Pair Distance of Repeated-Root Constacyclic Codes of Prime Power Lengths
On the Symbol-Pair Distance of Repeated-Root Constacyclic Codes of Prime Power Lengths
Source title:
IEEE Transactions on Information Theory, 64(4): 2417-2430,
2018
(ISI)
Academic year of acceptance:
2018-2019
Abstract:
Let p be a prime, and λ be a nonzero element of the finite field F pm . The λ-constacyclic codes of length p s over F pm 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 pm [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.