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On self-dual cyclic codes over finite fields

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 ... 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 …

Constacyclic and quasi-twisted Hermitian self-dual codes over finite fields

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: 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 … strike industries cobra tactical foregrip https://charltonteam.com

On Self-Dual Cyclic Codes Over Finite Fields IEEE Journals

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 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 … 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. strike industries discount code

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

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On self-dual cyclic codes over finite fields

On $ \sigma $-self-orthogonal constacyclic codes over $ \mathbb …

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 … 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

On self-dual cyclic codes over finite fields

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Web1 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 … 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 …

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. 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 …

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 … 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).

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

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 … strike industries end plate castle nutWeb14 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 … strike industries customer serviceWeb1 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 … strike industries golf ball launcherWebNew MDS self-dual codes over finite fields 33 We recall that a cyclic code C of length n over Fq is an ideal of the ring R = Fq[x]/(xn −1) generated by a polynomial g(x) which divides xn −1.C is uniquely deter- mined by its defining set T ={0 ≤ i ≤ 1 g αi = 0}, where α is an nth primitive root of the unity. The set T is then a union of cyclotomic classes C(j) … strike industries cookie cutter flushWebexistence 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 strike industries dual folding stockWeb1 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 … strike industries extended latchWeb29 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 . strike industries folding brace