Generalized hamming weights
WebJul 1, 2024 · The rth relative generalised Hamming weight (RGHW) of an linear code C and an subcode , a generalisation of generalised Hamming weight (GHW), characterises …
Generalized hamming weights
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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 … WebNov 19, 2024 · Motivated by the concepts of the relative generalized Hamming weight and the greedy weight, the relative greedy weight is introduced, and then it is shown that the codes achieving the upper bounds on the relative greedy weight are optimal on the security of the transmitted data symbols in the wire-tap channel. Based on such applications, the ...
WebJun 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 … Web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
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. These codes appeared re WebApr 1, 1999 · Definition 2: The generalized Hamming weight (distance) of order. of the code. over a finite alphabet set of size. will be defined as the index of the th nonzero value of the sequence. That is ...
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 …
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}. lansing dental officeWebGeneralized Hamming weights for linear codes Abstract: 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 … henderson county gov ncWebMotivated 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 … lansing eisenhower fitness centerWebGENERALIZED 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 … lansing dental office medicaidWebThe 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 … henderson county gun purchase permitWebThe 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. On the other hand, … henderson county habitatWebHamming weight is used in several disciplines including information theory, coding theory, and cryptography. In modular exponentiation by squaring, the number of modular … henderson county government