On self-dual cyclic codes over finite fields
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 … 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 …
On self-dual cyclic codes over finite fields
Did you know?
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 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 …
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 … 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 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. 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).
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
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.: crystal springs customer log inWeb1 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 ... dynacraft mckinney txWeb29 de jan. de 2012 · There is a one-to-one correspondence between -quasi-cyclic codes over a finite field and linear codes over a ring . Using this correspondence, we prove that every -quasi-cyclic self-dual code of length over a finite field can be obtained by the {\it building-up} construction, provided that char or , is a prime , and is a primitive element of . crystal springs cross country course mapWeb14 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 … dyna craft motor yachtWebThe 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 ... dynacraft outcast bikeWebIn 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 codes - linear codes over rings. Fu crystal springs dairycrystal springs customer service phone number