Classification of (16,6,2)-designs by ovals
type: Item
instance of: scholarly article
title: Classification of (16,6,2)-designs by ovals
zbMATH Open document ID: 0548.05009
DOI: 10.1016/0012-365X(84)90069-4
author: Natwar N. Roghelia
author: Sharad Sane
published in: Discrete Mathematics
publication date: 1984-01-01T00:00:00Z
review text: The three biplanes of order four (i.e. with \(k=6)\) have received a number of treatments, the first by Hussain forty years ago. Algebraic coding theory brought the ovals of these designs into prominence and the reviewer and \textit{C. Salwach} [Int. J. Math. Math. Sci. 2, 261-281 (1979; Zbl 0424.05009)] treated them from that point of view. (The authors seem not to have aware of that treatment and their methods are entirely combinatorial.) They give an ab initio development of these designs showing along the way that such a design contains 12, 28, or 60 ovals and that there is precisely one such design in each case. The treatment is elementary (but not straightforward) and gives a new approach to these designs. The methods are intrinsic to the parameter set and do not generalize. Such generalization as is available arises out of algebraic coding theory, the ovals being the minimal-weight vectors in the dual code. In Theorem 5.4 read ''deleting'' for ''detecting''.
Mathematics Subject Classification ID: 05B05
zbMATH DE Number: 3873338
zbMATH Keywords: biplanes
zbMATH Keywords: ovals
MaRDI profile type: Publication
cites work: Q4133993
cites work: Ovals in projective designs
cites work: Biplanes
cites work: Q3863891
cites work: On designs
cites work: Q5836508
cites work: Characterization of biplanes by their automorphism groups
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cites work: On extensions of nets
description: scientific article; zbMATH DE number 3873338