Some minimal cyclic codes over finite fields

Author: srpk

August undefined, 2024

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 Preparata non-linear (15, 8) code with the minimum distance 53). Moreover, by adding an overall parity bit to the Preparata non-linear (15, 8) code, a non- WebKeywords – Coding theory, cyclic codes, decoding, ideal theory, Gröbner bases, characteristic sets. INTRODUCTION. One important objective in coding theory has always …

A class of minimal cyclic codes over finite fields

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 … WebHow do you determine if an elliptic curve over a finite field is cyclic? Ask Question Asked 9 years, 11 months ago. Modified 7 years, ... Use the following code in Magma: F:=GF(11); E:=EllipticCurve([0,0,0,2*F.1,2*F.1]); ... Counting the Number of Points on … can dcm in dogs be reversed

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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. WebApr 26, 2024 · p ~ ( x) = x 6 + x 5 + 1 = x 6 p ( 1 x). From this we see immediately α − 1 and α − 2 are zeros of the factor p ~ ( x). So we have shown that α j is a zero of the generator … 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 + … fish number generator

New Explicit Good Linear Sum-Rank-Metric Codes

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 … WebUsing similar techniques, we show that a cyclic code over a large field may be embedded in a Grassmannian over a smaller field, while preserving cyclicity and multiplying the minimal distance by some ... vol. 59, pp. 7268–7277, 2013. [24] J. von zur Gathen, “Irreducible trinomials over finite fields,” Mathematics of Computation ... fish number 17 in fortniteWebJan 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 … fishnure reviews

"Webnonlinear binary codes are actually related to linear extended cyclic codes over the ring Z 4 [1]. Us-ing a spectral approach and a generalization of the results of [2], Dougherty and … " - Some minimal cyclic codes over finite fields

Some minimal cyclic codes over finite fields

qm+1 SOME RESULTS ON BCH CODES OF LENGTH

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 … 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 rings . After a brief description of the s…

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WebIn 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 ...

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 … 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 …

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 … WebFeb 14, 2024 · minimum distance of cyclic code. Ask Question Asked 1 month ago. Modified 30 days ago. ... finite-fields; it.information-theory; coding-theory; Share. Cite. Improve this …

WebThe 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 …

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 … c and c motors liverpoolWebApr 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 ... fish nursery operationWebthe 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 … candcnc torch raisingWebApr 1, 2024 · Due to their efficient encoding and decoding algorithms, cyclic codes, a subclass of linear codes, have applications in communication systems, consumer … fishnut chartersWebFinally, 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 c and c motors riverside njWebSOME RESULTS ON BCH CODES OF LENGTH q m+1 2 5 Example 1. Let q= 3, m= 5 and 0 ≤i≤121. ... C. Ding and S. Li,LCD cyclic codes over finite fieldsIEEE Trans. Inf. Theory, , 63 (2024), ... M. Shi, D. Huang, L. Sok and P. Sol´e,Double circulant LCD codes over Z 4, Finite Fields Appl., 58 (2024), 133-144. SOME RESULTS ON BCH CODES OF LENGTH q m+ ... c and c motorcycles charitonWebMay 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 ... can dc motors can be polyphase