On self-dual cyclic codes over finite fields

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August undefined, 2024

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 ... 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 ...

arXiv:1705.06049v1 [cs.IT] 17 May 2024

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. 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 … how much should painting a room cost

New MDS Self-dual Codes over Finite Fields of Odd Characteristic

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 … 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. 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 … how do they balance tires

Finite Fields and Their Applications - CORE

On self-dual cyclic codes over finite chain rings

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 … 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 … how do they attach hair extensionsWebA 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 much should parents pay for college

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

On self-dual cyclic codes over finite fields

On cyclic and negacyclic codes of length 8ℓmpn over finite field ...

Web1 de abr. de 2011 · Self-dual linear codes over finite fields form an interesting class of linear codes that have been extensively studied due to their nice algebraic structures … 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 …

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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 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. …

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 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 …

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 … 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) …

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:

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 … how much should parents give as wedding giftWeb1 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.: how do they beat bohemian rhapsodyWeb31 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: how do they beat bohemian rhapsody jjbaWeb15 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 … how do they beat wonder of uhttp://match.stanford.edu/reference/coding/sage/coding/cyclic_code.html how do they behaveWeb1 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 … how do they attach hernia meshWeb30 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 … how much should platelets increase with unit