On self-dual cyclic codes over finite fields

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 generation of optimal LCD codes and comparatively new quantum codes. It is worth noting that the ring in [21] is a specific form of our fundamental ring ℛ (for γ ... 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.

Two Dimensional $\left( \alpha,\beta \right) $-Constacyclic Codes …

Web11 de abr. de 2024 · Characterizations and constructions of such divisors are given together with their enumeration formulas. As applications, various properties of complementary dual and self-dual cyclic and negacyclic codes over finite fields are discussed in terms of SRIM and SCRIM factors of \(x^n-1\). Gervy Marie Angeles (Modelling and Applications … 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 … nothing changes in french https://beyondthebumpservices.com

New MDS self-dual codes over finite fields 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. 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 … Web29 de jan. de 2012 · There is a one-to-one correspondence between -quasi-cyclic codes over a finite field and linear codes over a ring . Using this correspondence, we prove that every -quasi-cyclic self-dual code of length over a finite field can be obtained by the {\it building-up} construction, provided that char or , is a prime , and is a primitive element of . how to set up google search console

On cyclic self-dual codes SpringerLink

Category:Repeated-root constacyclic codes of length $ 6lp^s

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On self-dual cyclic codes over finite fields

New MDS Self-dual Codes over Finite Fields of Odd Characteristic

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 ... 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 …

On self-dual cyclic codes over finite fields

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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 … WebOn Self-Dual Cyclic Codes over Finite Fields Yan Jia, San Ling, Chaoping Xing Abstract In coding theory, self-dual codes and cyclic codes are important classes of codes …

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 … WebIn 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

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. Web18 de jul. de 2024 · Title: Enumeration of Self-Dual Cyclic Codes of some Specific Lengths over Finite Fields

Web1 de mar. de 2014 · It is also proven that a self-dual code over a finite chain ring cannot be the lift of a binary cyclic self-dual code. The number of cyclic self-dual codes over chain rings is also investigated as an extension of the number of cyclic self-dual codes over finite fields given recently by Jia et al. References Abualrub T., Oehmke R.:

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 … nothing chords the scriptnothing chords townesWeb1 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 … nothing chilling at the holiday innWebA 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 … nothing chords liveWeb19 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 … how to set up google voice for businessWebSELF-DUAL SKEW-CYCLIC CODES OVER FINITE FIELDS IRWANSYAH, INTAN MUCHTADI-ALAMSYAH, AHMAD MUCHLIS, ALEAMS BARRA, AND DJOKO SUPRIJANTO Abstract. In this paper, we give the enumeration formulas for Euclidean self-dual skew-cyclic codes over finite fields when (n, θ ) = 1 and for some cases nothing chords rexWebLet 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 . nothing chords uke