Some minimal cyclic codes over finite fields

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 … WebIt is well known that every nonzero cyclic code of length n is the sum of some minimal cyclic codes of length n over Fq, which were widely investigated in Refs.[1–4]. Arora and Pruthi …

A class of minimal cyclic codes over finite fields

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 … incoterms difference between 2010 and 2020 https://steffen-hoffmann.net

How do you determine if an elliptic curve over a finite field is cyclic?

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 … WebSep 1, 2014 · 2014_Some minimal cyclic codes over finite fields.pdf. Content uploaded by Guanghui Zhang. Author content. All content in this area was uploaded by Guanghui … 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 … incoterms examen

A geometric characterization of minimal codes and their …

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Some minimal cyclic codes over finite fields

On the Construction of Quantum and LCD Codes from Cyclic Codes over …

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 … 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 …

Some minimal cyclic codes over finite fields

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WebDec 31, 2024 · M. Bonini and M. Borello, Minimal linear codes arising from blocking sets, Journal of Algebraic Combinatorics, 2024, 1–15. doi: 10.1007/s10801-019-00930-6. [13] … 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 ...

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 … WebJan 2024 - Mar 20241 year 3 months. San Francisco Bay Area. - Tech Lead on SDV reaction time and system latency. - Work on autonomy system challenges in self driving vehicles. - …

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 … 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 ...

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 …

WebJan 1, 2024 · Download Citation On Jan 1, 2024, Jiayuan Zhang and others published Some results on BCH codes of length $ \frac{{{q^m} + 1}}{2} Find, read and cite all the research you need on ResearchGate incoterms exmWebApr 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. incoterms exempleWebApr 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 … incoterms export schweizWebApr 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. incoterms exw bedeutungWebApr 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 ... incoterms explained pdfWeb20.1.12 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 … incoterms explained 2021WebPolycyclic 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 … incoterms explication