On self-dual cyclic codes over finite fields

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August undefined, 2024

WebFinally, we give some examples of self-dual, isodual, MDS and quasi-twisted codes corresponding to two-dimensional $(\alpha,\beta )$-constacyclic codes. Skip to search form Skip to main content Skip to account menu Web15 de jun. de 2014 · Self-dual and complementary dual cyclic/abelian codes over finite fields form important classes of linear codes that have been extensively studied ... {\rm GR}(p^r,s)[G]$ are established. The analogous results for self-dual and complementary dual cyclic codes over Galois rings are therefore obtained as corollaries. Comments: 22 ...

On self-dual cyclic codes over finite chain rings SpringerLink

Web31 de ago. de 2024 · In this paper, we generalize the notion of self-orthogonal codes to σ -self-orthogonal codes over an arbitrary finite ring. Then, we study the σ -self-orthogonality of constacyclic codes of length p s over the finite commutative chain ring F p m + u F p m, where p is a prime, u 2 = 0 and σ is an arbitrary ring automorphism of F p m + u F p m. graphics card freezes computer

On Self-Dual Cyclic Codes Over Finite Fields IEEE Transactions on ...

WebIn coding theory, self-dual codes and cyclic codes are important classes of codes which have been extensively studied. The main objects of study in this paper are self-dual … Web1 de abr. de 2024 · We examine cyclic codes over a finite commutative non-chain ring ℛ = F q [ u, v] / 〈 u 2 − γ u, v 2 − ϵ v, u v − v u 〉 for γ, ϵ ∈ F q * and its relevance in the … Web1 de jan. de 2024 · Employing a duality-preserving Gray map, self-dual and LCD codes of length 4n over F q are constructed. ... Güneri C Özkaya B Solé P Quasi-cyclic complementary dual codes Finite Fields Their Appl. 2016 42 67 80 3550383 10.1016/j.ffa.2016.07.005 Google Scholar Digital Library; 8. graphics card fun fact

New MDS self-dual codes over finite fields SpringerLink

Some Results on Linear Codes over ℤ4+vℤ4 - Semantic Scholar

WebA trace formula for quasi-cyclic codes over rings of characteristic not coprime with the co-index is derived. The main working tool is the Generalized Discrete Fourier Transform (GDFT), which in turn relies on the Hasse derivative of polynomials. A characterization of Type II self-dual quasi-cyclic codes of singly even co-index over finite fields of even … Web3 de mar. de 2011 · In this paper we construct MDS Euclidean and Hermitian self-dual codes which are extended cyclic duadic codes or negacyclic codes. We also construct Euclidean self-dual codes which are extended negacyclic codes. Based on these constructions, a large number of new MDS self-dual codes are given with parameters … graphics card for windows 10 laptopWebIn coding theory, quasi-twisted (QJ) codes form an important class of codes which has been extensively studied. We decompose a QT code to a direct sum of component codes - linear codes over rings. Fu chiropractic works raleigh nc

"Web15 de abr. de 2024 · Cyclic code is one important type of codes. This type of codes over finite field Fq can be considered as ideals in quotient ring Fq[x] xn−1 , where n is the length of codes. Based on this point of view, we can determine generator of any cyclic code, its Euclidean dual, and its dimension. Moreover, in some cases, we can also design the … " - On self-dual cyclic codes over finite fields

On self-dual cyclic codes over finite fields

On self-dual constacyclic codes over finite fields - ResearchGate

Web30 de abr. de 2024 · For any odd prime p, the structures and duals of λ -constacyclic codes of length 8 p s over R = F p m + u F p m are completely determined for all unit λ of the form λ = ξ l ∈ F p m, where l is even. In addition, the algebraic structures of all cyclic and negacyclic codes of length 8 p s over R are established in term of their generator … Web1 de mar. de 2024 · Let 픽q be finite field with q elements, where q be power of an odd prime p. In this paper, we determine generator polynomials of all cyclic and negacyclic codes of length 8ℓmpn over 픽q, ... On self-dual cyclic codes over finite fields, IEEE Trans. Inf. Theory 57(4) (2011) 2243–2251.

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Webexistence of cyclic self-dual codes of length 2rm over F 2s were studied independently by Kai and Zhu [10] and Jia et al. [11]. Jia et al. also determined the existence and the number of cyclic self-dual codes forq =2m. In this paper, we investigate repeated root cyclic and nega-cyclic codes of length prm over Fps with (m,p)=1. When Web31 de out. de 2015 · Abstract. Constacyclic and quasi-twisted Hermitian self-dual codes over finite fields are studied. An alternative algorithm for factorizing x n − λ over F q 2 is given, where λ is a unit in F q 2. Based on this factorization, the dimensions of the Hermitian hulls of λ -constacyclic codes of length n over F q 2 are determined.

Web1 de mar. de 2024 · In this paper, LCD cyclic, self dual and isodual codes over finite chain rings are investigated. It was proven recently that a non-free LCD cyclic code … Web19 de jul. de 2013 · On self-dual constacyclic codes over finite fields. This paper is devoted to the study of self-dual codes arising from constacyclic codes. Necessary and …

Web14 de mar. de 2011 · Abstract: In coding theory, self-dual codes and cyclic codes are important classes of codes which have been extensively studied. The main objects of study in this paper are self-dual cyclic codes over finite fields, i.e., the intersection of these … http://match.stanford.edu/reference/coding/sage/coding/cyclic_code.html

Web31 de jan. de 2024 · Our goal of this paper is to find a construction of all ℓ-quasi-cyclic self-dual codes over a finite field Fq of length mℓ for every positive even integer ℓ. In this …

WebMaximum distance separable (MDS) self-dual codes have useful properties due to their optimality with respect to the Singleton bound and its self-duality. MDS self-dual codes … graphics card game crashingWeb1 de abr. de 2011 · Self-dual linear codes over finite fields form an interesting class of linear codes that have been extensively studied due to their nice algebraic structures … graphics card for xboxWeb1 de jan. de 2024 · In Theorem 3.1, we have proved that, when q ≡ 3 ( mod 4), there exists an MDS self-dual code of length n = p e + 1 where e is an odd integer. This gives a … graphics card from chinaWeb30 de abr. de 2013 · G. K. Bakshi and M. Raka, Self-dual and self-orthogonal negacyclic codes of length $2p^n$ over a finite field, Finite Fields Appl., 19 (2013), 39-54.doi: 10.1016/j.ffa.2012.10.003. [2] chiropractic x-rayWeb1 de abr. de 2011 · The main objects of study in this paper are self-dual cyclic codes over finite fields, i.e., the intersection of these two classes. We show that self-dual cyclic … chiropractic works york meWeb1 de abr. de 2011 · In coding theory, self-dual codes and cyclic codes are important classes of codes which have been extensively studied. The main objects of study in this paper are self-dual cyclic codes over finite fields, i.e., the intersection of … chiropractic x ray analysisWebLet be a cyclic code of length =C over the binary eld F2.Put"() = 6+3+1.enwehave @() = 3 1.Wecanseethat has dimension and generating matrix is given by % ß D 100100100 010010010 001001001 E. ( ) Hence, a parity-check matrix for is given by B ß & ' ' ' ' * 100100000 010010000 001001000 000100100 000010010 000001001 - 5 5 5 5 7 . chiropractic x ray certification