Symbol-Pair Distance of Repeated-Root Constacyclic Codes of Prime Power Lengths over \({{\mathbb{F}_{p^m}[u]}/{\langle u^3\rangle}}\) [PDF]
Mathematics, 2021 Let p be a prime, s, m be positive integers, γ be a nonzero element of the finite field Fpm, and let R=Fpm[u]/⟨u3⟩ be the finite commutative chain ring.
Mohammed E. Charkani +3 more
doaj +4 more sources
On Symbol-Pair Distance of a Class of Constacyclic Codes of Length 3ps over
Axioms, 2023 Let p≠3 be any prime. In this paper, we compute symbol-pair distance of all γ-constacyclic codes of length 3ps over the finite commutative chain ring R=Fpm+uFpm, where γ is a unit of R which is not a cube in Fpm.
Hai Q. Dinh +2 more
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Maximum Distance Separable Codes for Symbol-Pair Read Channels [PDF]
IEEE Transactions on Information Theory, 2013 We study (symbol-pair) codes for symbol-pair read channels introduced recently by Cassuto and Blaum (2010). A Singleton-type bound on symbol-pair codes is established and infinite families of optimal symbol-pair codes are constructed.
Chengmin Wang +5 more
core +5 more sources
Constructions of MDS symbol-pair codes with minimum distance seven or eight [PDF]
Designs, Codes and Cryptography, 2022 Symbol-pair codes are proposed to guard against pair-errors in symbol-pair read channels. The minimum symbol-pair distance plays a vital role in determining the error-correcting capability and the constructions of symbol-pair codes with largest possible minimum symbol-pair distance is of great importance.
Junru Ma, Jinquan Luo
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MDS Constacyclic Codes and MDS Symbol-Pair Constacyclic Codes
IEEE Access, 2021 Symbol-pair codes are used to protect against symbol-pair errors in high density data storage systems. One of the most important tasks in symbol-pair coding theory is to design MDS codes.
Hai Q. Dinh +3 more
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Two Classes of Reducible Cyclic Codes With Large Minimum Symbol-Pair Distances
IEEE Transactions on Information Theory, 2023 The high-density data storage technology aims to design high-capacity storage at a relatively low cost. In order to achieve this goal, symbol-pair codes were proposed by Cassuto and Blaum \cite{CB10,CB11} to handle channels that output pairs of overlapping symbols.
Xiaoqiang Wang +3 more
openaire +3 more sources
Constructions of maximum distance separable symbol-pair codes using cyclic and constacyclic codes [PDF]
Designs, Codes and Cryptography, 2016 Symbol-pair code is a new coding framework which is proposed to correct errors in the symbol-pair read channel. In particular, maximum distance separable (MDS) symbol-pair codes are a kind of symbol-pair codes with the best possible error-correction capability.
Li, Shuxing, Ge, Gennian
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Hamming and Symbol-Pair Distances of Constacyclic Codes of Length 2ps over Fpm[u,v]⟨u2,v2,uv−vu⟩ [PDF]
SymmetryLet R=Fpm[u,v]⟨u2,v2,uv−vu⟩, where p is an odd prime and m is a positive integer. For a unit α in R, α-constacyclic codes of length 2ps over R are ideals of R[x]⟨x2ps−α⟩, where s is a positive integer. The structure of α-constacyclic codes are classified on the distinct cases for the unit α: when α is a square in R and when it is not.
Divya Acharya +2 more
semanticscholar +4 more sources
A Family of Almost MDS Symbol-Pair Codes of Length 8p
IEEE AccessIn high-density data storage systems, symbol-pair codes are commonly used to prevent symbol-pair errors. Designing maximum distance separable (MDS) codes is crucial in symbol-pair coding theory because MDS symbol-pair codes are the best at meeting the ...
Hai Q. Dinh +3 more
doaj +2 more sources