Notes on the value function
type: Item
instance of: scholarly article
title: Notes on the value function
zbMATH Open document ID: 1185.94088
author: Wende Chen
author: Zihui Liu
published in: Designs, Codes and Cryptography
publication date: 2010-02-25T00:00:00Z
review text: The purpose of this paper is to show some important properties of the value function, and then apply them to linear codes. In fact, the value function was first introduced by \textit{W. Chen} and \textit{T. Kløve} [IEEE Trans. Inf. Theory 42, No. 6, Pt. 2, 2265--2272 (1996; Zbl 0872.94044)], and it was used to construct the generator matrix of a linear code so as to determine the generalized Hamming weight. The relative generalized Hamming weight was first introduced in 2005 by Luo, Chaichana, Han Vinck and Chen [\textit{Y. Luo}, IEEE Trans. Inf. Theory 51, No. 3, 1222--1229 (2005; Zbl 1297.94035)]. The value function can also be generalized to study the relative generalized Hamming weight of a linear code and its subcodes.
Mathematics Subject Classification ID: 94B05
zbMATH DE Number: 5675120
zbMATH Keywords: generalized Hamming weight
zbMATH Keywords: relative generalized Hamming weight
zbMATH Keywords: value function
zbMATH Keywords: finite projective geometry
reviewed by: Bai Kishan Dass
MaRDI profile type: Publication
full work available at URL: s10623-009-9305-z
OpenAlex ID: W2061360910
cites work: The weight hierarchies of q-ary codes of dimension 4
cites work: The relative generalized Hamming weight of linear \(q\)-ary codes and their subcodes
cites work: Some New Characters on the Wire-Tap Channel of Type II
cites work: Generalized Hamming weights for linear codes
DOI: 10.1007/S10623-009-9305-Z
description: scientific article; zbMATH DE number 5675120