On the weight structure of reed-muller codes
WebIn the present paper, we give the Assmus--Mattson type theorem for near-extremal Type I and even formally self-dual codes. We show the existence of $1$-designs or $2$-designs for these codes. As a corollary, we prove the uniqueness of a self-orthogonal $2$-$(16,6,8)$ design. Web23 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 …
On the weight structure of reed-muller codes
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WebReed–Muller codes are linear block codes that are locally testable, locally decodable, and list decodable. These properties make them particularly useful in the design of … 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 ...
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 … WebReed-Muller Codes: Theory and Algorithms Emmanuel Abbe Amir Shpilka Min Ye Abstract Reed-Muller (RM) codes are among the oldest, simplest and perhaps most ubiquitous …
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] 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 …
WebThe weight distribution of GRM (generalized Reed-Muller) codes is unknown in general. This article describes and applies some new techniques to the codes over F3. Specifically, we decompose GRM codewords into words from smaller codes and use this decomposition, along with a projective geometry technique, to relate weights occurring in one code with …
WebOn the weight structure of Reed-Muller codes Abstract: The following theorem is proved. ... This theorem completely characterizes the codewords of the \nu th-order Reed-Muller code whose weights are less than twice the minimum weight and leads to the weight … great eastern human resourceWeb4-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 ... great eastern hotel restaurantWebThe weight distribution is a fundamental parameter of Reed-Muller codes. For second order q-ary Reed-Muller codes, their weight distributions have been computed in [11] for q= 2 and in [8] for ... great eastern hwWeb27 de jul. de 2024 · The minimum weight code word of RM(m,m) is 1, and there are m minimum weight code words in RM(m,m). Let x be one of the minimum weight code words in RM(m,m). Assume that x has 1 in jth position. If we delete the jth column of , then with high probability. Thus, there are indices of reducing the dimensions of C by 1. great eastern id loginWebINFORMATION ANJ) CONTaOL 14, 442-456 (1969) Restrictions on Weight Distribution of Reed-Muller Codes E. R. BERLEKAlV/P ANn N. J. A_. SLOANE Bell Telephone … great eastern idWebIEEE 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 … great eastern idtechWebReed-Muller Codes Reed-Muller codes are among the oldest known codes and have found widespread applications. ... Therefore, if r < m, R(r,m) contains code words of even weight only. Pf: We prove this by induction on m. Clearly, R(0,1) = {00,11} consists of all binary words of length 2 with even weight. Assume that this is true for R(m-2, great eastern hwy wa