MDS Symbol-Pair Repeated-Root Constacylic Codes of Prime Power Lengths over 𝔽pm C u𝔽pm
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Publication Details
Author list: Dinh H.Q., Kumam P., Kumar P., Satpati S., Singh A.K., Yamaka W.
Publisher: Institute of Electrical and Electronics Engineers
Publication year: 2019
Journal: IEEE Access (2169-3536)
Volume number: 7
Start page: 145039
End page: 145048
Number of pages: 10
ISSN: 2169-3536
eISSN: 2169-3536
Languages: English-Great Britain (EN-GB)
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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 R D 𝔽pm C uFpm (u2 = 0). The units of the ring R are of the form α + uβ and , where α; γ; 2 𝔽∗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. © 2013 IEEE.
Keywords
constacyclic codes, finite chain ring, MDS codes, Repeated-root codes, symbol-pair distance
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