On the weight structure of reed-muller codes
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 following properties [1] (p. xxviii): Fhas a fine structure, … 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).
On the weight structure of reed-muller codes
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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 … 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 …
WebThe 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 ... 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, …
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 ... WebFor various applications of DNA computing like DNA-based data storage, DNA codes are studied with properties such as avoiding secondary structures and satisfying Reversible …
WebThere are exactly two non-equivalent [32,11,12] -codes in the binary Reed-Muller code {\cal{RM}}(2,5) which contain {\cal{RM}}(1,5) and have the weight set \{0,12,16 ...
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 … comminuted hip fxWeb15 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] comminuted hill-sachs fractureWeb1 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 … comminuted humerus fracture icd 10Web27 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 … comminuted humeral head fracture icd 10Web24 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 … comminuted humeral head fracture treatmentWeb1.1 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 ... comminuted humerus fractureWeb19 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 … comminuted iliac fracture