On self-dual cyclic codes over finite fields

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WebA new algebraic approach to quasi-cyclic codes is introduced. The key idea is to regard a quasi-cyclic code over a field as a linear code over an auxiliary ring. By the use of the … 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

On the Construction of Quantum and LCD Codes from Cyclic Codes over …

WebThe only linear cyclic self-dual codes of length p over GR(p2,m) are p and (u −1)p−1 + p 2,p(u −1). Proof. If b = 0thenobviouslyp is self-dual. The case b = 1 leads to the invertible 1 ×1matrix M(p,1)=(2), and hence we obtain the self-dual code 1(u −1)p−1 + p 2,p(u −). Now we determine self-dual ideals in I for p =3 and small ... WebFinite Fields and Their Applications. Volume 63, March 2024, 101648. Self-reciprocal and self-conjugate-reciprocal irreducible factors of x n − λ and their applications. Author links open overlay panel Yansheng Wu a b c, Qin Yue a b, Shuqin Fan b. ... (SR) or self-conjugate-reciprocal (SCR). can i generate my own barcode

Existence conditions for self-orthogonal negacyclic codes over finite ...

Web7 de nov. de 2024 · In this paper, we produce new classes of MDS self-dual codes via (extended) generalized Reed-Solomon codes over finite fields of odd characteristic. Among our constructions, there are many MDS self-dual codes with new parameters which have never been reported. 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.: 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 … can i generate hdfc credit card pin online

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On the algebraic structure of quasi-cyclic codes .I. Finite fields

Web22 de fev. de 2024 · LCD Cyclic Codes Over Finite Fields. Abstract: In addition to their applications in data storage, communications systems, and consumer electronics, linear complementary dual (LCD) codes-a class of linear codes-have been employed in cryptography recently. LCD cyclic codes were referred to as reversible cyclic codes in … 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 … fitting ashcroft lockerWeb15 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 ... fitting a router to a router table

"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 … " - On self-dual cyclic codes over finite fields

On self-dual cyclic codes over finite fields

Web1 de jun. de 1999 · [Show full abstract] Terms: Codes over rings, Cyclic codes, Self-dual codes, Gray map. 1 Introduction Among the four rings of four elements, the Galois field … 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 …

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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 … 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 …

Web(a subset of) the defining set of the cyclic code (3) For now, only single-root cyclic codes are implemented. That is, only cyclic codes such that its length $n$ and field order $q$ are coprimes. Depending on which behaviour you want, you need to specify the names of the arguments to CyclicCode. See EXAMPLES section below for details. INPUT: Web31 de dez. de 2011 · 1. It is of interest to know when cyclic self-orthogonal codes of length n over F q do not exist. The conditions, listed by Pless in [7] under which cyclic self-orthogonal codes can not exist, are not always sufficient. An example is given to assert this. Here we give the necessary and sufficient conditions under which cyclic self …

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 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 …

Web1 de jan. de 2024 · As an application, we list all 589 self-dual cyclic codes over F 2 + u F 2 of length 24 precisely. Section 6 concludes the paper. 2. Explicit representation for self …

Web1 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 … fitting a shallow shower trayWebFinally, we give some examples of self-dual, isodual, MDS and quasi-twisted codes corresponding to two-dimensional $(\alpha,\beta )$-constacyclic codes. Skip to search … can i generate my own qr codeWeb1 de mar. de 2024 · So all free cyclic codes of length n = 3724 are LCD codes. 4. Self dual cyclic codes over finite chain rings. Let R be a finite chain ring with maximal ideal … fitting a shower domeWebIn 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 … fitting a shotgun recoil padWeb1 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 … can i germinate a tree rootWeb31 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. fitting a shower baseWebIn 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 … fitting a shower bar