Some minimal cyclic codes over finite fields

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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 … WebMar 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 ...

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WebIn mathematics, a finite field or Galois field (so-named in honor of Évariste Galois) is a field that contains a finite number of elements.As with any field, a finite field is a set on which … 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 … grantham art prize

On the Construction of Skew Quasi-Cyclic Codes^†

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 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 ... WebJan 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 … grantham arts council

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

On some bounds on the minimum distance of cyclic codes over …

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 … 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 … grantham army baseWebFukshansky, 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 … grantham art supplies blackpool

"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. " - Some minimal cyclic codes over finite fields

Some minimal cyclic codes over finite fields

qm+1 SOME RESULTS ON BCH CODES OF LENGTH

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

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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 ... 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 …

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 … WebFinite Fields and Their Applications. Volume 63, March 2024, 101633. Asymptotically good Z p r Z p s-additive cyclic 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 …

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 chipboard 3 ring binderWebC. 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 … grantham a\u0026eWebSince 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. grantham a\\u0026e phone numberWebOn Some Bounds of Minimum Distances of Cyclic Codes Over Finite Fields . 19 0 Download (0) 0 Download (0) chip board 8x10WebSOME 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 … chipboard 6x4WebFeb 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 … chipboard 4x8WebPolycyclic 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 … chipboard 50pt