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MDS Symbol-Pair Repeated-Root Constacylic Codes of Prime Power Lengths Over Fpm + uFpm

Authors: 

H. Q. Dinh, P. Kumam, P. Kumar, S. Satpati, A. K. Singh, W. Yamaka

Source title: 
IEEE Access, 2019 (ISI)
Academic year of acceptance: 
2019-2020
Abstract: 

MDS codes have the highest possible error-detecting and error-correcting capability among codes of given length and size. Let p be any prime, and s, m be positive integers. Here, we consider all constacyclic codes of length ps over the ring A. The units of the ring A are of the form α + and γ , where α, β, γ ∈ a, which provides pm(pm − 1) constacyclic codes. We acquire that the (α + )-constacyclic codes of ps length over a are the ideals a, of the finite chain ring aand the γ -constacyclic codes of ps length over a are the ideals of the ring a which is a local ring with the maximal ideal a, but it is not a chain ring. In this paper, we obtain all MDS symbol-pair constacyclic codes of length ps over a. We deduce that the MDS symbol-pair constacyclic codes are the trivial ideal a and the Type 3 ideal of γ -constacyclic codes for some particular values of p and s. We also present several parameters including the exact symbol-pair distances of MDS constacyclic symbol-pair codes for different values of p and s.