Some minimal cyclic codes over finite fields

Author: eocp

August undefined, 2024

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 … 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 - ScienceDirect

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

MDS CODES FROM POLYCYCLIC CODES OVER FINITE FIELDS

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. 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 + … 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 iowa county assessor website

$Soc. INDUST. MATH. Vol. Printed U.S.A. OVER FIELDS*$

Several classes of new projective three-weight or four-weight …

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- 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. iowa county by addressWebJan 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 … oosters orthodox pasen

"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. " - Some minimal cyclic codes over finite fields

Some minimal cyclic codes over finite fields

finite fields - How to calculate the minimum distance of a cyclic …

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

Did you know?

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 … 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 …

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 … 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 …

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 … 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

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 …

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 … oosters orthodoxWebin some cases, such codes can be decoded faster than other linear codes using nearest neighbor decoding. In [6], necessary and sufficient conditions for cyclic codes to be … oosthavensWebApr 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. iowa county attorney association jobsWebIn 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 ... oosterwold tiny houseWebFukshansky, 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 … oosthout chineesWebPOLYNOMIAL 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 … oostfront wo2WebPolycyclic 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 … iowa county cancer coalition