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Some minimal cyclic codes over finite fields

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 … WebAn irreducible code is a cyclic code in which the code, as an ideal is irreducible, i.e. is minimal in , so that its check polynomial is an irreducible polynomial. Examples [ edit ] For …

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

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] … 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 … fishing trips va beach va https://inline-retrofit.com

On the Construction of Skew Quasi-Cyclic Codes^†

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+ ... WebApr 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. WebJan 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 … fishing trips plymouth uk

NEW QUANTUM AND LCD CODES FROM CYCLIC CODES OVER A FINITE …

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

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Some minimal cyclic codes over finite fields

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

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

Some minimal cyclic codes over finite fields

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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 … 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 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 ... 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 …

WebJan 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 … 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 …

WebUsing similar techniques, we show that a cyclic code over a large field may be embedded in a Grassmannian over a smaller field, while preserving cyclicity and multiplying the minimal distance by some ... vol. 59, pp. 7268–7277, 2013. [24] J. von zur Gathen, “Irreducible trinomials over finite fields,” Mathematics of Computation ...

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 … fishing trips vancouver islandWebApr 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. cancer research uk main purposeWebJan 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. - … fishing trips to alaska vacationWebApr 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. fishing trips to patagoniaWebthe 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 … cancer research uk legacy faqsWebMar 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 ... fishing trips santa cruzWebMinimal 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 … cancer research uk melanoma