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 ... 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 …
On self-dual cyclic codes over finite fields
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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 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 …
WebSELF-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 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 …
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 … 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 …
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.
WebNew 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) … popular fgfgfgfgfgfgnow on bingWeb31 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 … shark handheld steam scrubber s3401 usesWeb7 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. … popular fidget toys for kidsWeb1 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 … popular festivals in italyWeb1 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.: popularfhfj now on bingWeb1 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 … popular fictionWeb7 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. popular fiction books 2016