Weight hierarchies of linear codes satisfying the chain condition
type: Item
instance of: scholarly article
title: Weight hierarchies of linear codes satisfying the chain condition
zbMATH Open document ID: 0913.94010
DOI: 10.1023/A:1008225524987
author: Wende Chen
author: Torleiv Kløve
published in: Designs, Codes and Cryptography
publication date: 1999-05-31T00:00:00Z
review text: This paper presents a sufficient condition for the existence of a code satisfying the chain condition with a given weight hierarchy. The weight hierarchy of a linear \([n,k;q]\) code \(C\) over \(\text{GF}(q)\) is the sequence \((d_1, d_2, \ldots, d_k)\) where \(d_r\) is the smallest support of an \(r\)-dimensional subcode of \(C\). \(C\) satisfies the chain condition if there exist subcodes \(D_r\) of \(C\) for \(1 \leq r \leq k\) such that \(\dim(D_r) = r\), \(w_s(D_r) = d_r\) and \(D_1 \subset D_2 \subset \cdots \subset D_k\). \(w_s(D)\) denotes the support weight of \(D\). A sequence \((a_1, a_2, \ldots,a_k)\) of positive integers is chain-good if it is the weight hierarchy of a code satisfying the chain condition. Theorem 1 gives an infinite class of chain-good sequences. This theorem is proved through explicit constructions. Theorem 2 provides additional chain-good sequences.
reviewed by: T. Aaron Gulliver
Mathematics Subject Classification ID: 94B05
zbMATH DE Number: 1230541
zbMATH Keywords: weight hierarchy
zbMATH Keywords: chain condition
zbMATH Keywords: support weight
zbMATH Keywords: chain-good sequences
MaRDI profile type: Publication
full work available at URL: a:1008225524987
OpenAlex ID: W1563812566
description: scientific article; zbMATH DE number 1230541