Strongly regular graphs from reducible cyclic codes
Sign Up to like & getrecommendations! Published in 2021 at "Journal of Algebraic Combinatorics"
DOI: 10.1007/s10801-020-01006-6
Abstract: Let p be a prime number. Reducible cyclic codes of rank 2 over $$\mathbb {Z}_{p^m}$$ Z p m are shown to have exactly two Hamming weights in some cases. Their weight distribution is computed explicitly.… read more here.
Keywords: reducible cyclic; cyclic codes; strongly regular; graphs ... See more keywords
On the Skew Cyclic Codes and the Reversibility Problem for DNA 4-Bases
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DOI: 10.1007/s11786-019-00424-5
Abstract: The DNA 4-bases are matched with the 256 elements of the finite ring $$R=F_{4}+uF_{4}+vF_{4}+uvF_{4}$$ R = F 4 + u F 4 + v F 4 + u v F 4 , where $$ u^{2}=u,v^{2}=v,uv=vu$$… read more here.
Keywords: reversibility problem; cyclic codes; problem dna; skew cyclic ... See more keywords
The symbol-pair distance distribution of a class of repeated-root cyclic codes over Fpm$\phantom {\dot {i}\!}\mathbb {F}_{p^{m}}$
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DOI: 10.1007/s12095-017-0249-2
Abstract: Symbol-pair codes are proposed to protect against pair errors in symbol-pair read channel. One main task in symbol-pair coding theory is to determine the minimum pair-distance of symbol-pair codes. In this paper, we investigate the… read more here.
Keywords: symbol pair; pair distance; pair; cyclic codes ... See more keywords
On the algebraic structure of quasi-cyclic codes of index 112$1\frac {1}{2}$
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DOI: 10.1007/s12095-019-0352-7
Abstract: In this paper, we study quasi-cyclic codes of index 112$1\frac {1}{2}$ and co-index 2m over Fq$\mathbb {F}_{q}$ and their dual codes, where m is a positive integer, q is a power of an odd prime… read more here.
Keywords: index 112; cyclic codes; quasi cyclic; 112 frac ... See more keywords
On $${\mathbb {Z}}_{2}{\mathbb {Z}}_{4}[\xi ]$$-skew cyclic codes
Sign Up to like & getrecommendations! Published in 2021 at "Journal of Applied Mathematics and Computing"
DOI: 10.1007/s12190-021-01580-3
Abstract: $${\mathbb {Z}}_2{\mathbb {Z}}_{4}$$ -additive codes have been defined as a subgroup of $${\mathbb {Z}}_2^{r}\times {\mathbb {Z}}_4^{s}$$ in [6] where $${\mathbb {Z}}_2$$ , $${\mathbb {Z}}_{4}$$ are the rings of integers modulo 2 and 4 respectively and… read more here.
Keywords: times mathbb; mathbb mathbb; cyclic codes; mathbb ... See more keywords
Quasi-cyclic codes: algebraic properties and applications
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DOI: 10.1007/s40314-020-1120-1
Abstract: In this paper, we provide criteria for the reversibility and conjugate-reversibility of 1-generator quasi-cyclic codes. The Chinese remainder theorem is used to provide a characterization for generalized quasi-cyclic codes to be Galois linear complementary-dual and… read more here.
Keywords: algebraic properties; codes algebraic; properties applications; cyclic codes ... See more keywords
Some Classes of New Quantum MDS and Synchronizable Codes Constructed From Repeated-Root Cyclic Codes of Length 6ps
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DOI: 10.1109/access.2021.3117561
Abstract: In this paper, we use the CSS and Steane’s constructions to establish quantum error-correcting codes (briefly, QEC codes) from cyclic codes of length $6p^{s}$ over $\mathbb F_{p^{m}}$ . We obtain several new classes of QEC… read more here.
Keywords: tex math; inline formula; cyclic codes;
A Generalized Parity-Check Transformation for Iterative Soft-Decision Decoding of Binary Cyclic Codes
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DOI: 10.1109/lcomm.2019.2956935
Abstract: The conventional parity-check matrix transformation algorithm (PTA) requires matrix inversion to transform matrices of maximum distance separable (MDS) codes. However, such matrix transformation is not always guaranteed for the class of non-MDS codes. Hence, the… read more here.
Keywords: binary cyclic; parity check; cyclic codes; parity ... See more keywords
Two Families of LCD BCH Codes
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DOI: 10.1109/tit.2017.2723363
Abstract: Historically, LCD cyclic codes were referred to as reversible cyclic codes, which had applications in data storage. Due to a newly discovered application in cryptography, there has been renewed interest in LCD codes. In this… read more here.
Keywords: two families; cyclic codes; bch codes; families lcd ... See more keywords
ℤ₂ℤ₄-Additive Quasi-Cyclic Codes
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DOI: 10.1109/tit.2021.3111858
Abstract: We study the codes of the title by the CRT method, that decomposes such codes into constituent codes, which are shorter codes over larger alphabets. Criteria on these constituent codes for self-duality and linear complementary… read more here.
Keywords: cyclic codes; additive quasi; quasi cyclic;
A Bound on the Minimal Field Size of LRCs, and Cyclic MR Codes That Attain It
Sign Up to like & getrecommendations! Published in 2023 at "IEEE Transactions on Information Theory"
DOI: 10.1109/tit.2022.3225953
Abstract: We prove a new lower bound on the field size of locally repairable codes (LRCs). Additionally, we construct maximally recoverable (MR) codes which are cyclic. While a known construction for MR codes has the same… read more here.
Keywords: cyclic codes; bound minimal; field size; minimal field ... See more keywords