On the minimum distance of cyclic codes

Author: vrjq

August undefined, 2024

WebKeywords: Finite elds, cyclic codes, trace representations, permutation polynomials. Abstract Estimation of the minimum distance of cyclic codes is a classical problem in … Web6.1.2 Cyclic Codes. The most commonly used class of linear block codes is the cyclic codes. Examples of cyclic codes ... (011110), (100110), (101101), (110011), and (111000). Determine the minimum weights and the minimum distance of the code. Solution. As reflected in the following table, the minimum Hamming weight for this linear …

On the minimum distance of ternary cyclic codes - Information …

Webgive a new proof to a result of [3] which says that the minimum distance, d min, for PAC codes is greater than or equal to the d min for polar codes. The usage of cyclic shifts in our work is motivated by the work of [4], which designs and analyzes a particular permutation set of polar codes relying on a N=4-cyclic shift for practical ... Web1 de jun. de 2024 · In this paper, we investigate the ternary cyclic codes with parameters [3m−1,3m−1−2m,4] based on some results proposed by Ding and Helleseth in 2013. Six new classes of optimal ternary cyclic... can disabled veterans have a roth ira

On the roots and minimum rank distance of skew cyclic codes

WebFor all binary cyclic codes of length < 63 (with two exceptions), we show that our methods yield the true minimum distance. The two exceptions at the end of our list are a code … Web1 de mar. de 1993 · On the minimum distance of ternary cyclic codes M. Eupen, J. H. Lint Published 1 March 1993 Computer Science IEEE Trans. Inf. Theory There are many ways to find lower bounds for the minimum distance of a cyclic code, based on investigation of the defining set. Some new theorems are derived. Webgive a new proof to a result of [3] which says that the minimum distance, d min, for PAC codes is greater than or equal to the d min for polar codes. The usage of cyclic shifts in … fish processing plant equipment

On the minimum distance of cyclic codes IEEE Journals

[PDF] Minimum Distance of PAC Codes v. Polar Codes Using Cyclic …

Web2 de mai. de 2024 · 1 Answer Sorted by: 1 The question should be the minimum distance is at least 4. (NTU final exam,right?) Suppose f ( x) is a nonzero codeword in C with weight at most 3, say f = a x i + b x j + c x k, where 0 ≤ i < j < k < n . Since g ( x) f ( x), then f ( α) = f ( α 2) = f ( α 3) = 0, so a α i l + b α j l + c α k l = 0, l = 1, 2, 3. WebA general algebraic method for decoding all types of binary cyclic codes is presented. It is shown that such a method can correct t=[(d-1)/2] errors, where d is the true minimum … can disabled veterans stay at navy lodgeWebSection 4 focuses on lower bounds for the minimum sum-rank distance of a cyclic-skew-cyclic code. We provide the analogues of the Roos bound and of the Hartmann-Tzeng bound, exploiting the notion of deﬁning sets for cyclic-skew-cyclic codes. In Section 5 we focus on tensor products of codes. We combine a cyclic code in the Hamming fish processing plant layout

"Webdistance of ternary cyclic codes. Furthermore, the exact minimum distance of ternary cyclic codes of length less than 40 is computed numerically. A table is given containing all ternary cyclic codes of length less than 40 and having a minimum distance exceeding the BCH bound. It seems that almost all lower bounds are equal to the minimum distance. " - On the minimum distance of cyclic codes

On the minimum distance of ternary cyclic codes - Information …

On the roots and minimum rank distance of skew cyclic codes

On the minimum distance of cyclic codes

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