MDS Symbol-Pair Repeated-Root Constacylic Codes of Prime Power Lengths over pm C u pm

• Main Authors: H. Q. Dinh, P. Kumam, P. Kumar, S. Satpati, A. K. Singh, W. Yamaka
• Format: Journal
• Published: 2020
• Subjects: Computer Science; Engineering; Materials Science
• Online Access: https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85075735293&origin=inward; http://cmuir.cmu.ac.th/jspui/handle/6653943832/67764
• Institution: Chiang Mai University

© 2013 IEEE. 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 R D pm C uFpm (u2 = 0). The units of the ring R are of the form α + uβ and , where α; γ; 2 ∗p m, which provides pm(pm-1) constacyclic codes. We acquire that the (α + uβ)-constacyclic codes of ps length over R are the ideals h(α0 x-1)ji, 0 ≤ j ≤ 2 ps, of the -nite chain ring R[x]=hxps (αC uβ)i and the-constacyclic codes of ps length over R are the ideals of the ring R[x]=hxps γ i which is a local ring with the maximal ideal hu; x γ 0i, but it is not a chain ring. In this paper, we obtain all MDS symbol-pair constacyclic codes of length ps over R. We deduce that the MDS symbol-pair constacyclic codes are the trivial ideal h1i and the Type 3 ideal of-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.