Results 1 to 10 of about 307,945 (311)
Quasi-Cyclic Subcodes of Cyclic Codes [PDF]
SIAM Journal on Discrete Mathematics, 2017 We completely characterize possible indices of quasi-cyclic subcodes in a cyclic code for a very broad class of cyclic codes. We present enumeration results for quasi-cyclic subcodes of a fixed index and show that the problem of enumeration is equivalent to enumeration of certain vector subspaces in finite fields.
Belfiore, Jean-Claude +2 more
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IEEE Transactions on Information Theory, 2013 submitted to IEEE Transactions on Information ...
Trautmann, Anna-Lena +3 more
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On Quasi-Cyclic Codes of Index 3. [PDF]
Entropy (Basel)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.
Abdukhalikov K, Shat RM.
europepmc +2 more sources
On Double Cyclic Codes over Finite Chain Rings for DNA Computing. [PDF]
Entropy (Basel)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.
Ali S +4 more
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Cyclic Sieving for cyclic codes [PDF]
Finite Fields and Their Applications, 2021 Prompted by a question of Jim Propp, this paper examines the cyclic sieving phenomenon (CSP) in certain cyclic codes. For example, it is shown that, among dual Hamming codes over $F_q$, the generating function for codedwords according to the major index statistic (resp. the inversion statistic) gives rise to a CSP when $q=2$ or $q=3$ (resp. when $q=2$).
Mason, Alex +2 more
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Inverse Quasi-Cyclic Codes and Automorphism Cyclic Codes
International Journal of Advanced Natural Sciences and Engineering Researches, 2023 Mustafa ÖZKAN
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Barekeng, 2021 Kode blok adalah skema penyandian yang menggunakan sistem kode-kode pada suatu lapangan hingga dengan panjang yang sama dan tetap. Kode blok linear atau lebih sering disebut kode linear atas suatu lapangan hingga merupakan himpunan kode-kode blok dengan ...
Juli Loisiana Butar-Butar +1 more
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On skew cyclic codes over $ M_{2}(\mathbb{F}_{2}) $
AIMS Mathematics, 2023 The algebraic structure of skew cyclic codes over $ M_{2} $($ \mathbb{F}_2 $), using the $ \mathbb{F}_4 $-cyclic algebra, is studied in this work. We determine that a skew cyclic code with a polynomial of minimum degree $ d(x) $ is a free code generated ...
Xuesong Si, Chuanze Niu
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On Optimal and Quantum Code Construction from Cyclic Codes over
Entropy, 2023 The key objective of this paper is to study the cyclic codes over mixed alphabets on the structure of FqPQ, where P=Fq[v]⟨v3−α22v⟩ and Q=Fq[u,v]⟨u2−α12,v3−α22v⟩ are nonchain finite rings and αi is in Fq/{0} for i∈{1,2}, where q=pm with m≥1 is a positive ...
Shakir Ali +5 more
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Describing a cyclic code by another cyclic code [PDF]
2012 IEEE International Symposium on Information Theory Proceedings, 2012 A new approach to bound the minimum distance of $q$-ary cyclic codes is presented. The connection to the BCH and the Hartmann--Tzeng bound is formulated and it is shown that for several cases an improvement is achieved. We associate a second cyclic code to the original one and bound its minimum distance in terms of parameters of the associated code.
Zeh, Alexander, Bezzateev, Sergey
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