Results 11 to 20 of about 70,163 (113)

On Quasi-Cyclic Codes of Index 3 [PDF]

Entropy
Quasi-cyclic codes of index 3 over finite fields are studied. We give a classification of such codes. Their duals with respect to the Euclidean and Hermitian inner products are investigated.
Kanat Abdukhalikov, Rasha M. Shat
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On Double Cyclic Codes over Finite Chain Rings for DNA Computing [PDF]

Entropy
Let e be a fixed positive integer and n1,n2 be odd positive integers. The main objective of this article is to investigate the algebraic structure of double cyclic codes of length (n1,n2) over the finite chain ring Re = F4e+vF4e, where v2=0.
Shakir Ali, Amal S. Alali, Mohd Azeem, Atif Ahmad Khan, Kok Bin Wong   +4 more
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Construction of reversible cyclic codes over 𝔽q + u𝔽q + u2𝔽q

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2023
Let q be a power of prime p. In this article, we investigate the reversible cyclic codes of arbitrary length n over the ring R = 𝔽q +u𝔽q + u2𝔽q, where u3 = 0 mod q.
Rehman Nadeem ur, Ahmad Mohammad Fareed, Azmi Mohd   +2 more
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A Straight Construction Algorithm for a Delay Invariant Convolutional Network Coding on Cyclic Networks

IEEE Access, 2022
Delay invariant convolutional network codes (abbreviated DI-CNCs) can guarantee multicast communication at asymptotically optimal rates in networks with any delay profile.
Xubo Zhao, Xiaoping Li
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Quasi-Cyclic Codes Via Unfolded Cyclic Codes and Their Reversibility

IEEE Access, 2019
The finite field $\mathbb {F}_{q^\ell }$ of $q^\ell $ elements contains $\mathbb {F}_{q}$ as a subfield. If $\theta \in \mathbb {F}_{q^\ell }$ is of degree $\ell $ over $\mathbb {F}_{q}$ , it can be used to unfold elements of $\mathbb {F}_{q^\
Ramy Taki Eldin, Hajime Matsui
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Applied quasi-cyclic LDPC codes from doubly-extended RS code and cyclic MDS code

Tongxin xuebao, 2008
Based on doubly-extended RS codes and cyclic MDS codes,two construction schemes were proposed for ap-plied quasi-cyclic LDPC codes whose Tanner graph is free of 4-cycles.In the first approach,all the nonzero codewords within a doubly-extended RS code ...
ZHANG Guo-hua, WANG Xin-mei
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Lower Bound on the Minimum Distance of Single-Generator Quasi-Twisted Codes

Mathematics, 2023
We recall a classic lower bound on the minimum Hamming distance of constacyclic codes over finite fields, analogous to the well-known BCH bound for cyclic codes.
Adel Alahmadi, Patrick Solé, Ramy Taki Eldin   +2 more
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Cyclic, LCD, and Self-Dual Codes over the Non-Frobenius Ring GR(p²,m)[u]/〈u²,pu〉

Mathematics
Let p be a prime number and m be a positive integer. In this paper, we investigate cyclic codes of length n over the local non-Frobenius ring R=GR(p2,m)[u], where u2=0 and pu=0.
Sami Alabiad, Alhanouf Ali Alhomaidhi
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MDS and MHDR Cyclic Codes over Finite Chain Rings

Journal of Mathematics
This work establishes a unique set of generators for a cyclic code over a finite chain ring. Towards this, we first determine the minimal spanning set and rank of the code.
Monika Dalal, Sucheta Dutt, Ranjeet Sehmi   +2 more
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Constructions and Enumerations of Self-Dual and LCD Double Circulant Codes over a Local Ring

Mathematics
The construction of self-dual and linear complementary dual (LCD) codes over finite rings, particularly over semi-local and local structures, is an active area of research due to their algebraic richness and applications in communications and ...
Sami H. Saif
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