On the minimum distance of cyclic codes
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