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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 _{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.