Results 11 to 20 of about 2,635,004 (136)
Polyadic Constacyclic Codes [PDF]
IEEE Transactions on Information Theory, 2014 For any given positive integer $m$, a necessary and sufficient condition for the existence of Type I $m$-adic constacyclic codes is given. Further, for any given integer $s$, a necessary and sufficient condition for $s$ to be a multiplier of a Type I ...
Chen, Bocong +3 more
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Application of Constacyclic codes to Quantum MDS Codes [PDF]
IEEE Transactions on Information Theory, 2014 Quantum maximal-distance-separable (MDS) codes form an important class of quantum codes. To get $q$-ary quantum MDS codes, it suffices to find linear MDS codes $C$ over $\mathbb{F}_{q^2}$ satisfying $C^{\perp_H}\subseteq C$ by the Hermitian construction ...
Chen, Bocong, Ling, San, Zhang, Guanghui
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Some Constacyclic Codes over Finite Chain Rings [PDF]
Advances in Mathematics of Communications, 2012 For $\lambda$ an $n$-th power of a unit in a finite chain ring we prove that $\lambda$-constacyclic repeated-root codes over some finite chain rings are equivalent to cyclic codes. This allows us to simplify the structure of some constacylic codes.
Batoul, Aicha +2 more
core +4 more sources
Skew Constacyclic Codes over a Non-Chain Ring. [PDF]
Entropy (Basel), 2023 In this paper, we investigate the algebraic structure of the non-local ring Rq=Fq[v]/⟨v2+1⟩ and identify the automorphisms of this ring to study the algebraic structure of the skew constacyclic codes and their duals over this ring. Furthermore, we give a necessary and sufficient condition for the skew constacyclic codes over Rq to be linear ...
Köroğlu ME, Sarı M.
europepmc +6 more sources
MDS Constacyclic Codes and MDS Symbol-Pair Constacyclic Codes [PDF]
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. MDS symbol-pair codes are optimal in the sense that such codes attain the Singleton bound. In this paper, a new class of MDS symbol-pair codes with code-length $5p$
Hai Q. Dinh +3 more
openaire +2 more sources
CONSTACYCLIC CODES OVER LIPSCHITZ INTEGERS
Matematički Vesnik, 2023 Summary: In this paper, the goal is to obtain constacyclic codes over Lipschitz integers in terms of Lipschitz metric. A decoding procedure is proposed for these codes, some of which have been shown to be perfect codes. Performance of constacyclic codes over Lipschitz integers is investigated over Additive White Gaussian Channel (AWGN) by means of ...
Guzeltepe, Murat +2 more
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Some Results on Images of a Class of λ-Constacyclic Codes Over Finite Fields
IEEE Access, 2020 In this paper, we show that any λ-constacyclic code over Fqm is a λ-constacyclic code over Fq under some special maps. Moreover, we show that the images of these λ_constacyclic codes can be put into the concatenated form.
Jian Gao, Juan Li, Yongkang Wang
doaj +1 more source
IEEE Access, 2020 Let p ≠ 3 be any prime. The structures of all λ-constacyclic codes of length 3ps over the finite commutative chain ring Fpm + uFpm (u2 = 0) are established in the term of their generator polynomials.
Hai Q. Dinh +2 more
doaj +1 more source
Repeated-Root Constacyclic Codes Over the Chain Ring Fpm[u]/⟨u3⟩
IEEE Access, 2020 Let Z = Fpm[u]/(u3) be the finite commutative chain ring, where p is a prime, m is a positive integer and Fpm is the finite field with pm elements. In this paper, we determine all repeated-root constacyclic codes of arbitrary lengths over Z and their ...
Tania Sidana, Anuradha Sharma
doaj +1 more source
Singleton-Optimal LRCs and Perfect LRCs via Cyclic and Constacyclic Codes [PDF]
Finite Fields Their Appl., 2023 Locally repairable codes (LRCs) have emerged as an important coding scheme in distributed storage systems (DSSs) with relatively low repair cost by accessing fewer non-failure nodes.
Weijun Fang +3 more
semanticscholar +1 more source