On the weight structure of reed-muller codes
Web27 de abr. de 2024 · Reed-Muller (RM) codes exhibit good performance under maximum-likelihood (ML) decoding due to their highly-symmetric structure. In this paper, we explore the question of whether the code symmetry of RM codes can also be exploited to achieve near-ML performance in practice. The main idea is to apply iterative decoding to a highly … Web1.1 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 ...
On the weight structure of reed-muller codes
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WebReed-Muller codes are error-correcting codes used in many areas related to coding theory, such as electrical engineering and computer ... Those upper bounds have been obtained … 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 ...
WebOur aim is the design of an efficient decoding algorithm in group codes. The algorithm is inspired by the well known syndrome decoding algorithm for l… Web19 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 …
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 … Web1 de jun. de 2024 · In particular, we give degree formulas for the generalized Hamming weights of Reed–Muller-type codes, and we determine the minimum distance of toric …
Web1 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 …
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. dating by numbers seriesWebHowever, it is important to remember that there are some limitations in using Reed–Muller codes since the choice of parameters does not have much freedom compared with BCH and Reed–Solomon codes. For Reed–Solomon codes, we see that they request probing with more energy, but such an increase of energy is less than 5 photons. dating cafe hildesheimWeb24 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 … dating by the signsWebAdditionally, 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 … dating by professionWebpolar codes (Section III) and Reed-Muller codes (Section V). The self-similar structure of these sets is also suggested in [6], which shows that polar and Reed-Muller codes are decreasing monomial codes. While [6] focuses on finite blocklengths, we study the properties of F for infinite blocklengths, i.e., for n → ∞. bjs in tysonsWebKeywords: 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 … dating cabinet cardsWebReed–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 ... bjs in stoughton