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

Authors: 

Hai Q. Dinh, Bac Trong Nguyen, Abhay Kumar Singh, and Songsak Sriboonchitta

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.