Some minimal cyclic codes over finite fields
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 ... 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.
Some minimal cyclic codes over finite fields
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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 … 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 …
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 … WebFirst, it is shown that self-dual cyclic codes of length nover F q exist if and only if qis a power of 2 and nis even. When these conditions are met, there is always a trivial self-dual cyclic …
WebThe wind farms extend over the entire domain width, and cyclic boundary conditions are applied in the y direction, so that the wind farms are effectively infinitely large in this … WebFeb 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 …
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
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+ ... hill walks in yorkshireWebApr 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 … smart business newsWebJun 7, 2024 · Shortened Linear Codes Over Finite Fields. Abstract: The puncturing and shortening techniques are two important approaches to constructing new linear codes … hill walks in shropshireWebJan 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 … smart business pack download for windows 10WebJan 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 … smart business optionsWebnonlinear binary codes are actually related to linear extended cyclic codes over the ring Z 4 [1]. Us-ing a spectral approach and a generalization of the results of [2], Dougherty and … hill walks in scotlandWebthe 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 … smart business pack website