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On the b-distance of repeated-root constacyclic codes of prime power lengths

Authors: 

Hai Q. Dinh, Xiaoqiang Wang, Hongwei Liu, Songsak Sriboonchitta

Source title: 
Discrete Mathematics, 343: 111780, 2020 (ISI)
Academic year of acceptance: 
2020-2021
Abstract: 

Let p be a prime, sm be positive integers, λ be a nonzero element of the finite field a. The b-distance generalizes the Hamming distance (= 1), and the symbol-pair distance (b = 2). While the Hamming and symbol-pair distances of all λ-constacyclic codes of length ps are completely determined, the general b-distance of such codes was left opened. In this paper, we provide a new technique to establish the b-distance of all λ-constacyclic codes of length ps, where 1≤≤ a. As an application, all MDS b-symbol constacyclic codes of length ps over aare obtained.