On self-dual cyclic codes over finite fields

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August undefined, 2024

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

Some new constructions of MDS self-dual codes over finite fields

Web1 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.: 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 … small united plane

On Self-Dual Cyclic Codes Over Finite Fields IEEE Transactions on ...

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. 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 … 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 … small united states flag image

LCD Cyclic Codes Over Finite Fields - IEEE Xplore

Two Dimensional $\left( \alpha,\beta \right) $-Constacyclic Codes …

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 … Web1 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 … hijinx festival outfitsWeb10 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. small united healthcare logo

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

On self-dual cyclic codes over finite fields

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

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 ... Web22 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 …

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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 … 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.

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) … 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 …

Web1 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 … Web1 de jan. de 2024 · In Theorem 3.1, we have proved that, when q ≡ 3 ( mod 4), there exists an MDS self-dual code of length n = p e + 1 where e is an odd integer. This gives a …

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

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 … hijinx philadelphia ticketsWebFinite 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). small united states flagsWebLet be a cyclic code of length =C over the binary eld F2.Put"() = 6+3+1.enwehave @() = 3 1.Wecanseethat has dimension and generating matrix is given by % ß D 100100100 010010010 001001001 E. ( ) Hence, a parity-check matrix for is given by B ß & ' ' ' ' * 100100000 010010000 001001000 000100100 000010010 000001001 - 5 5 5 5 7 . small united states map printableWeb(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: small united way logoWeb1 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 … hijinx family entertainment jonesboro arWeb1 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. small united states mapWeb11 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 … hijinx music festival 2021