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; ... 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.

(PDF) Skew cyclic Linear codes over 𝑹 = 𝑅 + 𝑤𝑅 + 𝑤2𝑅

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 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 … diabetes statistics in north dakota https://leesguysandgals.com

A class of minimal cyclic codes over finite fields

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 … 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 ... 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. diabetes statistics in pennsylvania

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Some minimal cyclic codes over finite fields

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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 … 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 …

Some minimal cyclic codes over finite fields

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WebMay 26, 2024 · Finally we construct a linear MSRD code over an arbitrary finite field ... \ldots, t-1$, for any given minimum sum-rank distance. There is no restriction on the block ... A sum-rank-metric code attaining the Singleton bound is constructed over some F q -linear MSRD code over some field F q with different matrix sizes n 1 > n 2 ... 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 …

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 · $\begingroup$ It would be easier to give a helpful answer, if you explained what you know about cyclic codes and Reed-Solomon codes. $\endgroup$ – Jyrki …

WebJun 7, 2024 · Shortened Linear Codes Over Finite Fields. Abstract: The puncturing and shortening techniques are two important approaches to constructing new linear 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+ ...

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 …

WebJan 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. - … cindy crawford with short hairWebApr 1, 2024 · Due to their efficient encoding and decoding algorithms, cyclic codes, a subclass of linear codes, have applications in communication systems, consumer … diabetes statistics in south africaWebAn 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 … cindy creed cpaWebnonlinear 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 … diabetes statistics in kenyaWebJan 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 cindy crawford wrinkle creamWebFinally, 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 diabetes statistics in the usWebA 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 … cindy crawford y rande gerber