On self-dual cyclic codes over finite fields

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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 ... 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.

On LCD, self dual and isodual cyclic codes over finite chain rings

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). 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 … dhl my business

New Construction of Maximum Distance Separable (MDS) Self …

http://match.stanford.edu/reference/coding/sage/coding/cyclic_code.html WebSome useful results on self-dual code over Rare given. Furthermore, the relationship between some comp lex unimodular lattices and Hermitian self-dual codes over R is given. Furthermore, the existing conditions of MDS codes overR is given, and the results show that there are no non-trivial MDS codes over R. Structural properties of cyclic codes are … 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. dhl muswell hill

$Constacyclic codes of length $ 8p^s $ over $ \mathbb F_{p^m}$

Cyclic code - Coding Theory - Stanford University

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 … 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 … dhl my rewardsWeb1 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 … dhl my english

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

On self-dual cyclic codes over finite fields

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

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. 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 …

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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 … 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. …

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 . 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 …

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 ... 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 …

Web1 de fev. de 2013 · Yang and Cai [27] gave necessary and sufficient conditions for the existence of Hermitian self-dual constacyclic codes of length n over a finite field F q 2 …

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 … cilantro engineering staffWeb10 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. dhl my clearanceWeb31 de mar. de 2024 · In this paper, we study constacyclic codes of length 6 l p s over finite field F q. The generator polynomials of all constacyclic codes and their duals are obtained. Moreover, we give the characterization and enumeration of linear complementary dual (LCD) and self-dual constacyclic codes of length 6 l p s over F q. Keywords: cilantro engineering londonWeb1 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 … cilantro creamy dressing recipeWeb(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: dhl myview payslipsWebS. Karadeniz and B. Yildiz, “New extremal binary self-dual codes of length 68 from R2-lifts of binary self-dual codes”, Advances in Mathematics of Communications, Vol. 7, No:2, pp. 219-229, 2013. 11. S. Karadeniz and B. Yildiz, “New Extremal Binary Self-dual codes of Length 66 as Extensions of self-dual codes over R_k”, Journal of the cilantro dish soap taste dhl my shipment