Some minimal cyclic codes over finite fields

WebRead Cyclic Codes over Finite Fields. Read Cyclic Codes over Finite Fields. ScienceGate; Advanced Search; Author Search; Journal Finder; Blog; Sign in / Sign up; ScienceGate; ... 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+ ...

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WebKeywords – Coding theory, cyclic codes, decoding, ideal theory, Gröbner bases, characteristic sets. INTRODUCTION. One important objective in coding theory has always … 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 … northern guild psychotherapy and counselling https://jpbarnhart.com

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

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 … 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. 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 … how to rob bank in roblox jailbreak

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

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Some minimal cyclic codes over finite fields

A class of minimal cyclic codes over finite fields

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 … 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 …

Some minimal cyclic codes over finite fields

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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 … 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 …

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 … 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 …

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 … 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 …

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…

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 … how to rob a safe in brookhaven rpWeblocal ring；cyclic codes；repeated-root codes；the number of codewords. 2010 MR Subject Classification：94B05；94B15. Document code：AArticle ID：0255-7797（2016）05 … how to rob a bank irlWebIn 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 ... northern guild of psychotherapyWebApr 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 … northern guitars reverbWebFeb 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 … northern guilford high school baseballWebJan 1, 2024 · $\begingroup$ It would be easier to give a helpful answer, if you explained what you know about cyclic codes and Reed-Solomon codes. $\endgroup$ – Jyrki … northern guild webmail loginWebMinimal 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 … how to rob a stagecoach without killing rdr2