Some minimal cyclic codes over finite fields

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August undefined, 2024

WebApr 1, 2024 · Kai and Zhu [29] later proposed a method for generating quantum codes using cyclic codes of odd length over the finite chain ring F 4 + v F 4 with u 2 = 0. Further, Qian [18] has introduced a method for generating quantum error-correcting codes using cyclic codes over the finite non-chain ring F 2 + v F 2 with arbitrary length v 2 = v. WebFukshansky, Lenny and David Kogan. “Cyclic and Well-Rounded Lattices.” Moscow Journal of Combinatorics and Number Theory, vol. 11, no. 1, 2024, pp. 79-96.. Abstract: We focus …

A class of minimal cyclic codes over finite fields

WebA Sequence Construction of Cyclic Codes over Finite Fields 3 2.1 Some notation and symbols ﬁxed throughout this paper Throughout this paper, we adopt the following … WebRecently, A. Zeh, A. Wachter-Zeh, M. Gadouleau and S. Bezzateev gave a method to obtain new lower bounds on the minimum distance of cyclic codes over finite fields. Here we … great plains checks didn\u0027t print

On the error-correcting pair for MDS linear codes with even minimum …

WebFlag codes that are orbits of a cyclic subgroup of the general linear group acting on flags of a vector space over a finite field, are called cyclic orbit flag codes. In this paper, we present a new contribution to the study of such codes, by focusing this time on the generating flag. More precisely, we examine those ones whose generating flag has at least one subfield … Weblocal ring；cyclic codes；repeated-root codes；the number of codewords. 2010 MR Subject Classification：94B05；94B15. Document code：AArticle ID：0255-7797（2016）05 … WebMar 2, 2016 · In this work, we construct cyclic polar codes based on a mixed-radix Cooley-Tukey decomposition of the Galois field Fourier transform. The programs developed for … great plains check printing

A class of minimal cyclic codes over finite fields

Double Cyclic Codes over \${\\mathbb{F}_{q}+v\\mathbb{F}_{q}}\$

WebA cyclic code has been one of the most active research topics in coding theory because they have many applications in data storage systems and communication systems. They have … WebMar 14, 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 … great plains characteristicsWebApr 10, 2010 · We show that the minimum distance of a linear code ... Our results hold for codes over every finite field, ... We also characterize the affine-invariant maximal extended cyclic codes. floor plan for windows

"WebC. Ding / Finite Fields and Their Applications 23 (2013) 8–34 9 any code C of length n over GF(q) corresponds to a subset of GF(q)[x]/(xn −1).The linear code C is cyclic if and only if … " - Some minimal cyclic codes over finite fields

Some minimal cyclic codes over finite fields

$Double Cyclic Codes over \${\\mathbb{F}_{q}+v\\mathbb{F}_{q}}\$$

WebFinite Fields and Their Applications. Volume 63, March 2024, 101633. Asymptotically good Z p r Z p s-additive cyclic codes WebFeb 1, 2015 · A class of minimal cyclic codes over finite fields @article{Chen2015ACO, title={A class of minimal cyclic codes over ... of the minimal cyclic codes of length 2pn …

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WebMinimal cyclic codes of length 2pn, Finite Fields Appl., 5(1999), 177-187. [1]], which considered the cases t= 1 and t= 2 respectively. We propose an approach di erent from … WebApr 1, 2024 · Due to their efficient encoding and decoding algorithms, cyclic codes, a subclass of linear codes, have applications in communication systems, consumer …

WebIn mathematics, a finite field or Galois field (so-named in honor of Évariste Galois) is a field that contains a finite number of elements.As with any field, a finite field is a set on which … WebIn this paper we study a special type of quasi-cyclic (QC) codes called skew QC codes. This set of codes is constructed using a non-commutative ring called the skew polynomial …

WebOn Some Bounds of Minimum Distances of Cyclic Codes Over Finite Fields . 19 0 Download (0) 0 Download (0) WebJul 5, 2013 · 1 Introduction. Cyclic codes over finite fields constitute a remarkable class of linear codes. In particular, some important codes, such as Hamming codes and BCH …

WebPOLYNOMIAL CODES OVER CERTAIN FINITE FIELDS* I. S. REEDAND G. SOLOMON; Introduction. Acode is a mappingfrom a vector space of dimension m over a finite field …

WebApr 10, 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. great plains chi alphaWebIn this paper, we study minimal cyclic codes of length $$\ell ^{m}$$ ℓ m over a finite field $$\mathbb{F }_q$$ F q , where $$\ell $$ ℓ is a prime divisor of $$q-1 ... floor plan for two story houseWebLet Fq be a finite field of odd order q and n=2ap1a1p2a2, where a,a1,a2 are positive integers, p1,p2 are distinct odd primes and 4p1p2 q1. In this paper, ... A class of minimal cyclic … great plains claims addressWebdecoding method [1]. Searching for minimal linear codes has been an interesting re-search topic in coding theory and cryptography. The following suﬃcient condition for a linear … floor plan for warehouseWebJan 6, 2024 · Any cyclic code of length n over F q is identified with exactly one ideal of the quotient algebra F q [ x] ∕ 〈 x n − 1 〉. A cyclic code is called minimal if the corresponding … floor plan for weddingWebPolycyclic codes are the generalization of cyclic and constacyclic codes and were studied in (William, 1972) for ... we construct polycyclic codes over finite fields by using same … great plains chemical lubbock texasWebThe wind farms extend over the entire domain width, and cyclic boundary conditions are applied in the y direction, so that the wind farms are effectively infinitely large in this … floor plan furniture