Some minimal cyclic codes over finite fields

WebOn Some Bounds of Minimum Distances of Cyclic Codes Over Finite Fields . 19 0 Download (0) 0 Download (0) 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 …

A sequence construction of cyclic codes over finite fields

WebFirst, it is shown that self-dual cyclic codes of length nover F q exist if and only if qis a power of 2 and nis even. When these conditions are met, there is always a trivial self-dual cyclic … WebSOME 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+ ... list of chief minister of himachal pradesh https://reesesrestoration.com

A NOTE ON CYCLIC CODES OVER Fpm+uFpm+u2Fpm_参考网

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- 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 … 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 … list of chief minister of uttarakhand

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

Category:Cyclic codes from cyclotomic sequences of order four

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Some minimal cyclic codes over finite fields

A class of minimal cyclic codes over finite fields

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 … 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 …

Some minimal cyclic codes over finite fields

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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 … WebSOME 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 …

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 … WebApr 1, 2024 · Due to their efficient encoding and decoding algorithms, cyclic codes, a subclass of linear codes, have applications in communication systems, consumer …

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 … Web20.1.12 Best Known Codes. Magma incorporates databases containing constructions of the best known linear codes over F q for q = 2,3,4,5,7,8,9.These databases contain codes of …

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 …

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. list of chief minister of maharashtra stateWebMar 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 this work can be accessed at https ... list of chief minister and governor of indiaWebHow 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 … list of chief ministers in indiaWebMar 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 … list of chief justicesWebKeywords – Coding theory, cyclic codes, decoding, ideal theory, Gröbner bases, characteristic sets. INTRODUCTION. One important objective in coding theory has always … list of chief ministers of all indian statesWebApr 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. images of trigeminal nerveWebDue 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 … list of chief minister of jharkhand