Linear codes associated with geometric structures
type: Item
instance of: scholarly article
title: Linear codes associated with geometric structures
zbMATH Open document ID: 0641.94017
DOI: 10.1007/BF03322406
published in: Results in Mathematics
publication date: 1987-01-01T00:00:00Z
review text: The author studies some codes obtained from geometric structures. Let S be the point set of the structure and let B be the set of blocks. Then he gives the following two codes: I) Code V is spanned by the characteristic functions of the blocks. II) \(H=\{X\in P(S)| \forall_{C\in B}| X\cap C| mod 2\) is constant\(\}\). K is the code obtained by considering the characteristic functions of the elements of H. He restates some results on dimension and minimum distance of the codes obtained by taking for (S;B) the projective plane. Furthermore he states some results (which he proved in another paper) on the dimension and minimum distance of the codes obtained by taking for (S;B): \(S=set\) of lines in PG(r,q) (AG)r,q)), \(B=set\) of stars of lines in PG(r,q) (AG(r,q)). (A star is the set of lines going through a fixed point).
Mathematics Subject Classification ID: 94B25
Mathematics Subject Classification ID: 94B05
Mathematics Subject Classification ID: 05B05
zbMATH DE Number: 4045639
zbMATH Keywords: geometric codes
zbMATH Keywords: characteristic functions of blocks
zbMATH Keywords: codes obtained from geometric structures
zbMATH Keywords: dimension
zbMATH Keywords: minimum distance
zbMATH Keywords: projective plane
author: Giuseppe Tallini
reviewed by: Herman J. Tiersma
MaRDI profile type: Publication
cites work: Q4074794
description: scientific article; zbMATH DE number 4045639