Generalized hamming weights
WebHamming weight is used in several disciplines including information theory, coding theory, and cryptography. In modular exponentiation by squaring, the number of modular … WebDec 30, 2016 · The generalized Hamming weights of a linear code have been extensively studied since Wei first use them to characterize the cryptography performance of a linear code over the wire-tap channel of type II. In this paper, we investigate the generalized Hamming weights of three classes of linear codes constructed through defining sets …
Generalized hamming weights
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Web摘要： Motivated by cryptographical applications, the algebraic structure, of linear codes from a new perspective is studied. By viewing the minimum Hamming weight as a certain minimum property of one-dimensional subcodes, a generalized notion of higher-dimensional Hamming weights is obtained. Weband support size _< n. The h-th generalized Hamming weight of C is then defined to be dh(C) := min{]_(D)[ : D is an h-dimensional subcode of C}. It is easy to see that all(C) denotes the traditional minimum distance or minimum Hamming weight of the code. The weight hierarchy of C can then be defined to be the set of integers {dh(C) : 1 < h <_ k}.
WebThe generalized Hamming weights of linear codes have attracted scholars' attention since Wei used them to characterize the cryptography performance of a linear code over the wire-tap channel of type II in 1991. Generally speaking, it is hard to determine linear codes' generalized Hamming weights, especially the weight hierarchy. ... WebApr 18, 2024 · Our approach is based on the observation that the generalized Hamming weights and the dimension/length profiles of a linear code form a Galois connection. The central result of this paper is a general Wei-type duality theorem for two Galois connections between finite subsets of , from which all the known Wei-type duality theorems can be …
WebMay 20, 1996 · The rth generalized Hamming weight of a code C is defined by dr(C) = min{lx(D)IID is an r-dimensional subcode of C}, The weight hierarchy ofa code C is the set ofgeneralized Hamming weights {dr ( C)}, 1 ~ r ~ k. The weight hierarchy has been determined for the Golay code, Reed-Muller codes by Wei [13], for codes meeting the … WebJun 17, 2015 · Abstract: The generalized Hamming weights d r (C) of a linear code C are a natural generalization of the minimum Hamming distance d(C)[=d 1 (C)] and have become an important research object in coding theory since Wei's originary work in 1991. In this paper, two general formulas on d(C) for irreducible cyclic codes are presented using …
WebAug 18, 2024 · In this paper, we discuss the generalized Hamming weights of a class of linear codes associated with non-degenerate quadratic forms. In order to do so, we study the quadratic forms over subspaces of finite field and obtain some interesting results about subspaces and their dual spaces. On this basis, we solve all the generalized Hamming …
WebMar 1, 1994 · 1991. TLDR. Results are presented on the generalized Hamming weights of several classes of binary cyclic codes, including primitive double- error-correcting and triple-error-Correcting BCH codes, certain reversible cycling codes, and some extended binary Goppa codes. 65. hemochromatosis and statinWebThe composition of a vector v ∈ FN is defined to be comp ( v) = s = ( s0, s1, …, sq−1 ), where si is the number of coordinates of v equal to ω i. Clearly . The Hamming weight … hemochromatosis blogWeb服务热线： 4008-161-200 800-990-8900. 国家科技图书文献中心. © Copyright(C)2024 NSTL.All Rights Reserved 版权所有 hemochromatosis antibodyWebThe generalized Hamming weights of a linear code are fundamental code parameters related to the minimal overlap structures of the subcodes. They were introduced by V.K. Wei (1991) and shown to characterize the performance of the linear code in certain cryptographical applications. Results are presented on the generalized Hamming … hemochromatosis and vitamin eWebGENERALIZED HAMMING WEIGHTS 125 0. INTRODUCTION Let F q be a finite field with q elements, where q is a power of the prime pschar F.For a linear wxn, k code C over F i.e., a linear subspace qq C:Fnof dimension k., it was Wei 21 who first introduced the notion ofwx q generalized Hamming weights d r for 1 F r F k which provide substantial information … l and w supply fort worth txWebMotivated by cryptographical applications, the algebraic structure, of linear codes from a new perspective is studied. By viewing the minimum Hamming weight as a certain minimum property of one-dimensional subcodes, a generalized notion of higher-dimensional Hamming weights is obtained. These weights characterize the code … l and w supply medway maWebJun 17, 2015 · Generalized Hamming Weights of Irreducible Cyclic Codes. Abstract: The generalized Hamming weights d r (C) of a linear code C are a natural generalization of … l and w supply fife wa