On self-dual cyclic codes over finite fields

Author: hgow

August undefined, 2024

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 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 ...

Self-dual Repeated Root Cyclic and Negacyclic Codes over Finite …

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 … how many ep in pokemon xy

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

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 … 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 … Web1 de set. de 2024 · Since MDS self-dual codes over finite field of even characteristic with any possible parameter have been found in .In this paper, we obtain some new results … how many epic fruits are there in king legacy

Review Article Skew Constacyclic Codes over Finite Fields and Finite …

On quasi-twisted codes over finite fields

Web25 de mai. de 2012 · 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 … 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 … high uibc and low iron saturationWeb15 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 ... high uggs

"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 … " - 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

WebLet 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 . 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

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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 … Web13 de jul. de 2012 · In this paper, we determine all self-dual, self-orthogonal and complementary-dual negacyclic codes of length 2pnℓm over the finite field Fq with q …

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 … 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.

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

Web30 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]

Web10 de abr. de 2024 · Over finite fields, cyclic codes have been extensively investigated (see, for example, [2,3,4,5] and references therein). In 2015, from the cyclic codes over F q + v F q + v 2 F q + v 3 F q (where q = p m, p is a prime such that 3 (p − 1), v 4 = v, and m is a positive integer), Gao et al. constructed new quantum codes over F q. how many ep the gloryWeb1 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 … how many ep naruto shippuden haveWeb7 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. how many ep of hazbin hotelWebA 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 … how many ep of loki are thereWeb11 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 … how many epc points for solar panelsWeb1 de fev. de 2015 · Necessary and sufficient conditions are given for the existence of Hermitian self-dual constacyclic codes over ... Xing C.: On self-dual cyclic codes … how many ep will blue lock haveWebIn 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 … how many ep of happiness kdrama