Some minimal cyclic codes over finite fields

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August undefined, 2024

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 … WebMay 26, 2024 · Finally we construct a linear MSRD code over an arbitrary finite field ... \ldots, t-1$, for any given minimum sum-rank distance. There is no restriction on the block ... A sum-rank-metric code attaining the Singleton bound is constructed over some F q -linear MSRD code over some ﬁeld F q with diﬀerent matrix sizes n 1 > n 2 ...

Asymptotically good ZprZps-additive cyclic codes - ScienceDirect

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. WebJan 1, 2024 · $\begingroup$ It would be easier to give a helpful answer, if you explained what you know about cyclic codes and Reed-Solomon codes. $\endgroup$ – Jyrki … how do you make a toilet flush stronger

A class of minimal cyclic codes over finite fields

WebAn irreducible code is a cyclic code in which the code, as an ideal is irreducible, i.e. is minimal in , so that its check polynomial is an irreducible polynomial. Examples [ edit ] For … 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 … WebSince every linear code is contained in an MDS linear code with the same minimum distance over some finite field extension, we focus our study on MDS linear codes. It is well-known that an MDS linear code with minimum distance 2 ℓ + 1 has an ℓ -error-correcting pair if and only if it is a generalized Reed-Solomon code. how do you make a tint

On Binary Linear (16, 8) Code with the Maximum Minimum Distance

arXiv:1611.06487v1 [cs.IT] 20 Nov 2016

WebIn this paper, let $ q $ be a power of a prime, we construct several classes of new projective three-weight or four-weight linear codes over $ \mathbb{F}_q $ from the defining sets construction, and determine their weight distributions by using additive character sums. Especially, these codes are suitable for applications in secret sharing schemes. WebLet 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 … how do you make a toneWebThe Gray weight of the elements of R and a Gray map from Rn to Z2n 4 are defined, which lead to the MacWillams identity of the linear code ove r R, and the results show that there are no non-trivial MDS codes over R. In this paper, we study the linear codes over the commutative ring R = Z4 + vZ4, wherev2 = v. We define the Gray weight of the elements … how do you make a timeline in powerpoint

"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 … " - Some minimal cyclic codes over finite fields

Some minimal cyclic codes over finite fields

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WebApr 14, 2024 · Hence the cyclic contraction potential grows if the material is dilating and decreases to a minimal value of zero in case of contraction. Including this contraction potential into Eq. 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

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WebDue to interpreted critical soil conditions with regard to cyclic loading and cyclic soil stiffness & strength degradation based on cyclic laboratory testing of sand and clay soil … 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 …

WebJan 6, 2024 · Minimal quadratic residue cyclic codes of length 2n. AbstractLetF be a finite field of prime power orderq (odd) and the multiplicative order ofq modulo 2n (n>1) be ϕ … WebSince the ring F q + v F q is a finite field locally, the results shown in this paper reflect some properties of double cyclic codes over finite fields locally as a result. Through some …

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. Webthe shortened (16, 8) code of this cyclic code has the minimum distance 5. There are also the very famous binary BCH code of (15, 7) with the minimum distance 5, and the …

Webdecoding 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 …

WebApr 14, 2024 · Thanks to it, tables are provided showing that sum-rank BCH codes beat previously known codes for the finite field of size $ 2^2 = 4 $ for the sum-rank metric for matrices with $ m=2 $ rows and ... how do you make a timeline on google slides how do you make a tom collinsWebA 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 … phone claim number verizonWebFeb 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 … phone claim phone number at\\u0026tWebJan 6, 2024 · This result is used to compute idempotent generators of minimal abelian codes, extending results of Arora and Pruthi [S.K. Arora, M. Pruthi, Minimal cyclic codes of … phone claim phone number at\u0026tWebFinite Fields and Their Applications. Volume 63, March 2024, 101633. Asymptotically good Z p r Z p s-additive cyclic codes how do you make a tote bagWebApr 1, 2024 · Due to their efficient encoding and decoding algorithms, cyclic codes, a subclass of linear codes, have applications in communication systems, consumer … how do you make a totem of undying