On the weight structure of reed-muller codes
WebAdditionally, we study the weight distribution of Reed-Muller codes. Prior results of Kasami and Tokura [8] on the structure of Reed-Muller codewords up to twice the minimum … Web14 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 …
On the weight structure of reed-muller codes
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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. … WebHá 2 dias · Optimal Testing of Generalized Reed-Muller Codes in Fewer Queries. April 2024; License; CC BY 4.0
WebIEEE Transactions on Information Theory. Periodical Home; Latest Issue; Archive; Authors; Affiliations; Home Browse by Title Periodicals IEEE Transactions on Information Theory Vol. 16, No. 6 On the weight structure of Reed-Muller codes Browse by Title Periodicals IEEE Transactions on Information Theory Vol. 16, No. 6 On the weight structure of Reed … Web1 de nov. de 2024 · These results show that RM codes of such degrees are in some sense close to achieving capacity, and show that, information theoretically, such codes can handle a fraction of $1/2-o(1)$ random errors with high probability. This work proves new results on the ability of binary Reed-Muller codes to decode from random errors and erasures. We …
Web4-linear Reed-Muller codes with the same parameters and properties as the usual binary linear Reed-Muller code are obtained with both de nitions. Key words: Plotkin construction, Reed-Muller codes, Z 4-linear codes. 1 Introduction The concept of Z 4-linearity of binary codes was pioneered by Nechaev in [10]. This result opened up a new ... WebReed-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.
Web194 IEEE TRANSACTIONS ON INFORMATION THEORY, VOL.40, NO. 1, JANUARY 1994 Restrictions on the Weight Distribution of Binary Linear Codes Imposed by the …
WebKeywords: 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 … pennyboard achsenWebHá 2 dias · Optimal Testing of Generalized Reed-Muller Codes in Fewer Queries. April 2024; License; CC BY 4.0 penny board at five belowWeb10 de nov. de 2024 · In this paper, subcodes constructed from Reed-Muller codes by removal of generator matrix rows are considered. ... Information Rates and Weights of Codes in Structural Matrix Rings. November 2001. pennyboard aus holzWeb19 de mar. de 2024 · Shuxing Li. The weight distribution of second order -ary Reed-Muller codes have been determined by Sloane and Berlekamp (IEEE Trans. Inform. Theory, … to buy a handgun you must be years oldWeb23 de abr. de 2008 · Abstract. Not much is known about the weight distribution of the generalized Reed-Muller code RM q ( s, m) when q > 2, s > 2 and m ≥ 2. Even the … penny board backpackWebReed-Muller-Codes-Matlab. A MATLAB function library containing encoders, decoders and weight enumerators for Reed-Muller codes. Overview. Reed–Muller codes are a class of error-correcting codes that are used in wireless communications applications [1, 2]. Each Reed-Muller code is defined using two integer parameters, r <= m, and is notated RM ... to buy a boatWeb1.1 Reed–Muller Codes Reed-Muller codes are a very fundamental and well studied family of codes. RM(n,d) is a linear code, whose codewords f∈RM(n,d):𝔽n 2 →𝔽2 are eval-uations of polynomials in nvariables of total degree at most dover 𝔽2. In this work we study the code RM(n,d)whend n, and are interested in particu-lar in the case ... penny board aesthetic