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On the minimum distance of cyclic codes

WebWe give a general lower bound for the minimum distance of $q$-ary quasi-cyclic codes of length $m\ell$ and index $\ell$, where $m$ is relatively prime to $q$. Web14 de abr. de 2024 · PDF On Apr 14, 2024, Karima Chatouh published Skew cyclic Linear codes over 𝑹 = 𝑅 + 𝑤𝑅 + 𝑤2𝑅 ... Sum-rank BCH codes, with prescribed minimum sum-rank distance, ...

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

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. 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 … ihear alexandra hills https://cervidology.com

On the error-correcting pair for MDS linear codes with even …

Web9 de jun. de 2015 · Decoding of Repeated-Root Cyclic Codes up to New Bounds on Their Minimum Distance Alexander Zeh, Markus Ulmschneider The well-known approach of Bose, Ray-Chaudhuri and Hocquenghem and its generalization by Hartmann and Tzeng are lower bounds on the minimum distance of simple-root cyclic codes. 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 … WebThe bound involves the minimum distances of constituent codes of length ℓ as well as the minimum distances of certain cyclic codes of length m which are related to the fields … i hear air when i press my brakes

On Generalized Galois Cyclic Orbit Flag Codes

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

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On the minimum distance of cyclic codes

On the error-correcting pair for MDS linear codes with even …

Web13 de mar. de 2014 · In coding theory estimating the minimum distance of a given code is one of the main problems, which has been studied by many researchers. Several bounds on the minimum distance are presented (such as Bose and Chaudhuri [ 1 ]; Hocquenghem [ 8 ]; Boston [ 3 ]; Hartmann and Tzeng [ 6 ]; Hartmann et al. [ 7 ]; Roos [ 9, 10 ]). WebKeywords: Finite elds, cyclic codes, trace representations, permutation polynomials. Abstract Estimation of the minimum distance of cyclic codes is a classical problem in …

On the minimum distance of cyclic codes

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WebFlag codes that are orbits of a cyclic subgroup of the general linear group acting on flags of a vector space over a finite field, are called cyclic orbit flag codes. In this paper, we present a new contribution to the study of such codes, by focusing this time on the generating flag. More precisely, we examine those ones whose generating flag has at least one subfield … WebAbstract: The minimum distance of a class of reversible cyclic codes has been proved to be greater than that given by the BCH bound. It is also noted that this class of codes …

Web10 de abr. de 2010 · We show that the minimum distance of a linear code ... We also characterize the affine-invariant maximal extended cyclic codes. Then by the CSS … 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 …

Web30 de nov. de 2024 · Published: February 2024 The authors are supported by NTU Research Grant M4080456 Abstract Two bounds on the minimum distance of cyclic … WebIndex Terms—Cyclic Code, Cyclic Product Code, Bound on the Minimum Distance, Efficient Decoding I. INTRODUCTION Cyclic codes play a central role in (distributed) …

Web30 de jun. de 2014 · And we also calculate the minimum distance of some cyclic codes and give lower bounds on the minimum distance for some other cyclic codes. Keywords: Cyclic codes, Whiteman generalized cyclotomic sequences, generator polynomial, minimum distance. Mathematics Subject Classification: Primary: 58F15, 58F17; …

WebThis bound is related to a second method for bounding the minimum distance of a cyclic code, which we call shifting. This method can be even stronger than the first one. For all … is the nc real estate exam hardWeb9 de ago. de 2024 · A cyclic code is a cyclic q-ary code of length n, constant weight w and minimum distance d.Let denote the largest possible size of a cyclic code. The pure … i hear all this music and it breaks my heartWeb12 de jul. de 2013 · Generalizing bounds on the minimum distance of cyclic codes using cyclic product codes Abstract: Two generalizations of the Hartmann-Tzeng (HT) bound … i hear a loud noiseWebcodes (0,) of dimension k, in F,G, and cyclic codes d, in the rclatcd fields F,, s E I. Then d = C3, E, (0,) 0 24, is a 2-D cyclic code of dimension E, E ,k;dim(M,j. We can easily derive a … is then conjunctionWebFor 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 … i hear america singing by walt whitman dateWeb26 de abr. de 2024 · We can thus conclude that the minimum distance of this code is d m i n = 6. It may be worth observing that because x + 1 is a factor of the generator, all the … i hear america singing genreWebSince t is small, we conclude that our algorithm will have the running time discussed above if d ^ is large. This is the case for quadratic residue codes, since a quadratic residue code is essentially self-dual, and is also the case for most BCH codes since the minimal distance of their dual can be estimated via the Carlitz-Uchiyama bound [5] and other techniques … i hear american singing赏析