Generalized hamming weights

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August undefined, 2024

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 WebOct 10, 2014 · Title: Generalized Hamming Weights of Irreducible Cyclic Codes Authors: Minghui Yang , Jin Li , Keqin Feng , Dongdai Lin Download a PDF of the paper titled Generalized Hamming Weights of Irreducible Cyclic Codes, by Minghui Yang and 3 …

[2107.07093] GHW-based Necessary and Sufficient Conditions for …

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 ... 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 commonwealth nccd

Generalized Hamming weights for linear codes - 百度学术

WebSep 1, 1992 · Wei [8] studied the minimum support weights (which he called generalized Hamming weights) in his analysis of the wire-tap channel of type II. His paper has sparked renewed interest in the subject. Further recent papers on the generalized Hamming weights (or minimum support weights) of binary codes are [1, 4]. WebThe 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 … 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 … commonwealth nephrology

A Galois Connection Approach to Wei-Type Duality Theorems

[2203.17194] Free Resolutions and Generalized Hamming Weights …

WebIn this paper, based on the theory of inverse Gray mapping, two classes of new generalized cyclotomic quaternary sequences with period pq are constructed, where pq is a product of two large distinct primes. In addition, we give the linear complexity over the residue class ring Z4 via the Hamming weights of their Fourier spectral sequence. WebMay 27, 2015 · The generalized Hamming weights introduced by Wei (1991) have been shown to be fundamental descriptive parameters of a linear block code. They have been found to be useful in certain cryptographic ... commonwealth nbn plansWebMar 31, 2024 · Free Resolutions and Generalized Hamming Weights of binary linear codes. Ignacio García-Marco, Irene Márquez-Corbella, Edgar Martínez-Moro, Yuriko Pitones. In this work, we explore the relationship between free resolution of some monomial ideals and Generalized Hamming Weights (GHWs) of binary codes. More precisely, we … commonwealth nbn

"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. " - Generalized hamming weights

Generalized hamming weights

On the weight hierarchy of the semiprimitive codes

WebJun 1, 1992 · In this paper, we first provide a general formula to compute the generalized Hamming weights of linear codes from the defining sets, which generalizes several … WebMotivated 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 …

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WebThe homogeneous weights of the elements of (Z 2 k) n are the Hamming weights of their images under the generalized Gray map. This homogeneous weight w G on Z 2 k is … 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 …

WebJun 2, 2024 · By the rth generalized Hamming weight of a linear code C, denoted by $ d_{r}(C) $, we mean the smallest support size of any r-dimensional subcode of C.In this paper, we determine the rth generalized Hamming weight of the binary linear code C(G) with the parity check matrix A(G) , where the underlying graph G is a complete graph, a … WebThe 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 …

WebMar 1, 2024 · Relative generalized Hamming weights (RGHWs) of a linear code with respect to a linear subcode determine the security of the linear ramp secret sharing scheme based on the linear codes. They can be used to express the information leakage of the secret when some keepers of shares are corrupted. Cyclic codes are an interesting type … 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. ...

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 …

duckworth animal hospitalWebThe 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, … commonwealth national golf club horsham paWebJul 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 code performances of wiretap channel of type II, secure network coding, linear ramp secret sharing scheme, trellis complexity etc.In this study, the authors investigate non … commonwealth nephrology framingham maWebOct 10, 2014 · Abstract:The generalized Hamming weight (GHW) $d_r(C)$ of linear codes $C$ is anatural generalization of the minimum Hamming distance $d(C)(=d_1(C))$ and … duckworth animal hospital greeneville tnhttp://www.uprh.edu/~simu/Reports2001/NOU.pdf duckworth ankenyWebJul 15, 2024 · In this paper we propose the necessary and sufficient conditions for support constrained generator matrices of general linear codes based on the generalized Hamming weights. It is proved that the direct generalization of the GM-MDS conjecture for $2$-MDS codes and algebraic geometry codes is not true over arbitrary fields. duckworth angela leeWebJun 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 … commonwealth nephrology weymouth ma