On the weight structure of reed-muller codes
Web15 de mai. de 2003 · For binary Reed–Muller codes the problems of finding the number of the minimal and non-minimal codewords of weight 2d min are equivalent, ... On the weight structure of Reed–Muller codes. IEEE Trans. Inform. Theory, IT-16 (6) (1970), pp. 752-759. View in Scopus Google Scholar [5] WebRather than relying on the precise structure of the codes, our method exploits code symmetry. ... On the weight enumeration of weights less than 2.5d of Reed-Muller codes. Inform. and Control, 30(4):380 – 395, 1976. Google Scholar Cross Ref; T. Kaufman, S. Lovett, and E. Porat. Weight distribution and list-decoding size of Reed-Muller codes.
On the weight structure of reed-muller codes
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Web9 de fev. de 2024 · Reed-Muller (RM) codes are among the oldest, simplest and perhaps most ubiquitous family of codes. They are used in many areas of coding theory in both electrical engineering and computer science. Yet, many of their important properties are still under investigation. This paper covers some of the recent developments regarding the … Web28 de mar. de 2024 · The weight distribution of second order q-ary Reed–Muller codes have been determined by Sloane and Berlekamp (IEEE Trans. Inform.Theory, vol. IT-16, …
Web1 de mai. de 1971 · Very little is known on the weight structure of subcodes of the 3rd or high order Reed-Muller code (or supercodes of the (m- 4)th or lower order Reed-Muller code). The following remark on the minimum weight code-words is a strengthened version of Theorem 11 in (Kasami-Lin- Peterson (1968a)). Web1.1 Reed-Muller Codes Reed-Muller (RM) codes were introduced in 1954, first by Muller [Mul54] and shortly after by Reed [Ree54] who also provided a decoding algorithm. They are among the oldest and simplest codes to construct — the codewords are multivariate polynomials of a given degree, and the en-coding function is just their evaluation ...
Web1 de jan. de 2024 · We will use these invariants to study the minimum distance and the Hamming weights of Reed–Muller-type codes over graphs. The edge biparticity and the edge connectivity are well studied invariants of a graph [16], [34]. In Section 2 we give an algebraic method for computing the edge biparticity (Proposition 2.3). Web24 de jun. de 2024 · Reed-Muller (RM) codes are among the oldest, simplest and perhaps most ubiquitous family of codes. They are used in many areas of coding theory in both …
WebWe study affine cartesian codes, which are a Reed-Muller type of evaluation codes, where polynomials are evaluated at the cartesian product of n subsets of a finite field F_q. …
WebOn the weight structure of Reed-Muller codes. T. Kasami, N. Tokura; Computer Science. IEEE Trans. Inf. Theory. 1970; TLDR. This theorem completely characterizes the … northern alaska toursWebReed–Muller code (1 ) for odd , whose minimum weight is greater thanorequaltotheso-calledquadraticbound.Somegeneralrestrictionson the weight distribution of a coset of (1 ) are obtained by partitioning its words according to their weight divisibility. Most notably, we show that there are exactly five weight distributions for optimal cosets of ... how to reward hard workWebReed-Muller codes are extensively studied for many years, but their metric properties, like the covering radius, are very elusive and are being discovered to this day; just recently, Wang has found the covering radius of the code RM(2;7) to be equal to 40 [22]. These problems put Reed-Muller codes in our focus of the research of metric regularity. northern alberta funeralWebOn the weight structure of Reed-Muller codes. Authors: T. Kasami. View Profile, N. Tokura. ... This theorem completely characterizes the codewords of the nu th-order Reed … how to reward employees without taxesWeb1 de mai. de 2011 · Borissov, N. Manev and S. Nikova [Discrete Appl. Math. 128, No. 1, 65–74 (2003; Zbl 1024.94010)] initiated the study of minimal codewords in the binary … northern alberta funerals obituariesWeb14 de nov. de 2008 · In this work we provide asymptotic bounds for the list-decoding size of Reed-Muller codes that apply for {\em all} distances. Additionally, we study the weight distribution of Reed-Muller codes. Prior results of Kasami and Tokura \cite {KT70} on the structure of Reed-Muller codewords up to twice the minimum distance, imply bounds … northern alberta fish speciesWebKeywords: polar codes; Reed–Muller codes; fractals; self-similarity 1. Introduction In his book on fractal geometry, Falconer characterizes a set Fas a fractal if it has some of the following properties [1] (p. xxviii): Fhas a fine structure, … northern alberta ent