On self-dual cyclic codes over finite fields

Author: mgaf

August undefined, 2024

http://match.stanford.edu/reference/coding/sage/coding/cyclic_code.html 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 …

Cyclic codes and self-dual codes over F2+uF2 - ResearchGate

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 … 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. batu bara gif

Repeated-root constacyclic codes of length $ 6lp^s

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 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: 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. batubara harga

Review Article Skew Constacyclic Codes over Finite Fields and Finite …

Constacyclic codes of length $ 8p^s $ over $ \mathbb 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 … 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). tifosi ajax a napoliWeb31 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 … batubara global energy

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

On self-dual cyclic codes over finite fields

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

Web29 de nov. de 2008 · We investigate cyclic self-dual codes over $${\mathbb{F}_{2^{r}}}$$ . ... An improved upper bound on self-dual codes over finite fields GF(11), GF(19), and … Web1 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 …

Did you know?

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 … 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.

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. Among our constructions, there are many MDS self-dual codes with new parameters which have never been reported. 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 …

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 … 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 …

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 …

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 ... batubara harga hari iniWeb7 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. … batubara hari iniWeb1 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 … batubara indonesia 2022Web1 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 ... tifosi juve a napoliWeb11 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 … batu bara hari iniWeb1 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.: tifr projectWeb31 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 … batubara indonesia buku