On the minimum distance of cyclic codes

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August undefined, 2024

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.

On some bounds on the minimum distance of cyclic codes over …

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 … Web10 de abr. de 2024 · The primary goal of this article is to study the structural properties of cyclic codes over a finite ring R=Fq[u1,u2]/ u12−α2,u22 −β2 ... In view of Theorem 7, … floor mats for toyota hilux

coding theory - Finding minimum distance of a cyclic code

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 … WebWe deal with the minimum distances of q -ary cyclic codes of length q m - 1 generated by products of two distinct minimal polynomials, give a necessary and sufficient condition for … WebThe main result is a new lower bound for the minimum distance of cyclic codes that includes earlier bounds (i.e., BCH bound, HT bound, Roos bound). This 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 binary cyclic codes … floor mats for toyota tundra 2008

ON THE MINIMUM DISTANCE OF CYCLIC CODES by LEYLA IS˘IK

On the Construction of Quantum and LCD Codes from 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) … Web25 de nov. de 2024 · The codes that achieve the optimal minimum pair distance (for given codeword length, code book size and alphabet) are called Maximum Distance Separable (MDS) symbol-pair codes. A way to study the minimum pair distance of a code is through its connection to the minimum Hamming distance of the code. floor mats for toyota tundra 2010Web6 de jun. de 2009 · A note on negacyclic and cyclic codes of length p s over a finite field of characteristic p (2009) (submitted). Google Scholar Salagean, A.: Repeated-root cyclic and negacyclic codes over a finite chain ring. great place it services

"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 $q$. " - On the minimum distance of cyclic codes

On the minimum distance of cyclic codes

Bounds on the Minimum Distance of Punctured Quasi-Cyclic LDPC …

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; … Webcodes (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 …

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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 … Web10 de mai. de 2011 · Decoding Cyclic Codes up to a New Bound on the Minimum Distance Alexander Zeh, Antonia Wachter, Sergey Bezzateev 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 and, for some codes, upon the Hartmann …

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 … Web26 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 …

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 ]). WebTheorem I: Let C, be a binary cyclic code of length n (odd) with generator gl(x), and let C, be a binary cyclic code of length n with generator g,(x)g,(x). Let di be the minimum distance of Ci, i = 1,2. Then the binary cyclic code C of length 2n with generator g:(x)g2(x) is equivalent to the IuIu + UI sum of C, and C,.

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 …

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 … floor mats for toyota truckWebIt turns out that lowest-code-rate cyclic codes with small minimum distances are useful for our approach. Therefore, we give a su cient condi-tion for binary cyclic codes of … great place in us for early november vacationWebSince 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 … floor mats for toyota tundra double cabWeb10 de abr. de 2024 · The primary goal of this article is to study the structural properties of cyclic codes over a finite ring R=Fq[u1,u2]/ u12−α2,u22 −β2 ... In view of Theorem 7, we conclude that there exists a quantum code [[120, 88, 3]] 5. which has the same minimum distance but a larger code rate than the best previously known ... great place north belfast redeemerWeb8 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 ... floor mats for trucks napaWeb1 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... floor mats for toyota venzaWeb26 de jan. de 2013 · Generalizing Bounds on the Minimum Distance of Cyclic Codes Using Cyclic Product Codes Alexander Zeh, Antonia Wachter-Zeh, Maximilien … great place in toronto