On the minimum distance of cyclic codes
Web10 de mai. de 2011 · A new lower bound on the minimum distance of q-ary cyclic codes is proposed. This bound improves upon the Bose-Chaudhuri-Hocquenghem (BCH) bound … WebSince 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 …
On the minimum distance of cyclic codes
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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 ]). 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.
Web7 de dez. de 1998 · It is desired to develop a method that can derive the weight distribution with high speed, or the minimum distance and the number of corresponding code words. Recently, Barg and Dumer [5] proposed a method in which the minimum distance and the number of corresponding code words are determined efficiently, by utilizing the … Web20 de jul. de 1996 · The BCH code of length 1023 and designed distance 253 has minimum distance 253. The cyclic codes of length 2 11 Gamma 1; 2 13 Gamma 1; 2 17 Gamma 1, with generator polynomial m 1 (x) and m 7 (x ...
WebFinally, we provide an upper bound on the minimum distance for nonbinary quasi-cyclic LDPC codes. areas of communications and signal processing, ... Lei Liu, Jie Huang, Wuyang Zhou, Shengli Zhou. "Computing the Minimum Distance of Nonbinary LDPC Codes." IEEE Transactions on Communications 60.7 (2012) 1753-1758 MLA; Harvard; … 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; …
Web8 de jun. de 2009 · The Minimum Hamming Distance of Cyclic Codes of Length 2p s. June 2009. DOI: 10.1007/978-3-642-02181-7_10. Conference: Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, 18th ...
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 … dachshund cell phone cord protectorWeb2 de mai. de 2024 · 2. My goal is to find a generator polynomial for a binary [ 15, 5, d] cyclic code that corrects all errors with weight less than or equal to 3. I have to find a degree 10 monic polynomial that divides x 15 − 1 ( mod 2) and has weight 7. If 15 and 5 were coprime I would know how to factor x 15 − 1 using cyclotomic theory. bin hire narre warrenWebIndex Terms—Cyclic Code, Cyclic Product Code, Bound on the Minimum Distance, Efficient Decoding I. INTRODUCTION Cyclic codes play a central role in (distributed) … bin hire melbourne south eastern suburbsWeb19 de mar. de 2013 · Bounds on the Minimum Distance of Punctured Quasi-Cyclic LDPC Codes Abstract: Recent work by Divsalar has shown that properly designed protograph … bin hire greensboroughWeb1 de set. de 2014 · The minimum Hamming distances of irreducible cyclic codes September 2014 Finite Fields and Their Applications 29:225–242 DOI: 10.1016/j.ffa.2014.05.003 Authors: Fengwei Li Qin Yue Nanjing... dachshund cat scratcherWebSince 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 … bin hire north shoreWebThis 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 … dachshund chihuahua mix puppies for sale