Nets and their codes
type: Item
instance of: scholarly article
title: Nets and their codes
zbMATH Open document ID: 0788.51015
DOI: 10.1007/BF01418529
author: Steven T. Dougherty
published in: Designs, Codes and Cryptography
publication date: 1994-05-26T00:00:00Z
review text: From author's abstract: ``In this paper finite nets [cfr. \textit{R. H. Bruck}, Pac. J. Math. 13, 421-457 (1963; Zbl 0124.009)] will be studied using the following linear codes: the row space of the incidence vectors of lines, the intersection of this code with its orthogonal, the code generated by differences of parallel lines, and the orthogonal to these codes. Using these codes we are able to recast the \textit{G. E. Moorhouse} conjecture [cfr. Des. Codes Cryptography 1, No. 1, 7-29 (1991; Zbl 0755.05020)] in terms of subcodes of the codes he uses, determine coding- theoretic reasons for a net's being maximal, and generalize a theorem of Assmus and Key which uses codes to classify finite planes of prime order.'' In the references read [7] instead of [12] and [8] instead of [13].
Mathematics Subject Classification ID: 51E22
Mathematics Subject Classification ID: 94B05
zbMATH DE Number: 474716
zbMATH Keywords: finite nets
zbMATH Keywords: linear codes
reviewed by: Giorgio Faina
MaRDI profile type: Publication
cites work: Affine and projective planes
cites work: Finite Nets, I. Numerical Invariants
cites work: Finite nets. II: Uniqueness and imbedding
cites work: Q3967545
cites work: Bruck nets, codes, and characters of loops
cites work: On the construction of finite projective planes from homology semibiplanes
full work available at URL: https://doi.org/10.1007/bf01418529
OpenAlex ID: W2002008598
description: scientific article; zbMATH DE number 474716