On self-dual cyclic codes over finite fields
Web31 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: 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).
On self-dual cyclic codes over finite fields
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WebS. 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 Web1 de mar. de 2024 · Let 픽q be finite field with q elements, where q be power of an odd prime p. In this paper, we determine generator polynomials of all cyclic and negacyclic codes of length 8ℓmpn over 픽q, ... On self-dual cyclic codes over finite fields, IEEE Trans. Inf. Theory 57(4) (2011) 2243–2251.
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 · 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 …
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 … 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 …
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 …
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 … hide the snowmanWeb31 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 … hide the status bar flutterWeb31 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 … hide the songWeb30 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 … hide the soulWeb1 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 ... hide the soul chuckyWeb22 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 … hide the soul gameWebSome 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 … hide the snake in the bush