On the minimum distance of cyclic codes
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. 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 …
On the minimum distance of cyclic codes
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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. Web26 de jan. de 2013 · Generalizing Bounds on the Minimum Distance of Cyclic Codes Using Cyclic Product Codes Alexander Zeh, Antonia Wachter-Zeh, Maximilien …
Web4 de abr. de 2024 · By using the cyclic shift matrices, this study provides new proof that, from the minimum distance viewpoint, PAC codes are superior to polar codes. The polarization-adjusted convolutional (PAC) codes are a new family of linear codes that can perform close to the theoretical bounds. These codes make use of both polar coding and … 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 …
WebSection 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 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 …
WebSince 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 …
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 … philips led t5 24w 840Webgive 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 … truth telling in dementiaWebIndex Terms—Cyclic Code, Cyclic Product Code, Bound on the Minimum Distance, Efficient Decoding I. INTRODUCTION Cyclic codes play a central role in (distributed) … philips led torchWeb6.1.2 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 … philips led troffer retrofit kitWebThis 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 of length < 63 (with two exceptions), we show that our methods yield … truth telling first nationWeb1 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. philips led tube 10wWebSince 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 … truth telling in ethics