Existence of \((q,6,1)\) difference families with \(q\) a prime power
type: Item
instance of: scholarly article
title: Existence of \((q,6,1)\) difference families with \(q\) a prime power
zbMATH Open document ID: 0912.05013
DOI: 10.1023/A:1008311600271
author: L. Zhu
author: Kejun Chen
published in: Designs, Codes and Cryptography
publication date: 1999-05-09T00:00:00Z
review text: A family \(\mathcal F\) of \(k\)-subsets of an additive group \(G\) of order \(v\) is called a \((v,k,1)\)-DF if any nonzero element of \(G\) can be represented in a unique way as difference of two elements of some member of \(\mathcal F\). If \(G\) is the additive group of \(\text{GF}(q)\) the necessary condition \(q\equiv 1\pmod {30}\) is also sufficient with the exception \(q=61\) only. The result is obtained using Wilson's ideas, character sums and computer search for \(q\in[10000,360191]\).
Mathematics Subject Classification ID: 05B10
Mathematics Subject Classification ID: 11T23
Mathematics Subject Classification ID: 05B05
zbMATH DE Number: 1230698
zbMATH Keywords: difference families
zbMATH Keywords: character sums
zbMATH Keywords: cyclotomic class
zbMATH Keywords: block designs
zbMATH Keywords: automorphisms of block designs
reviewed by: Giovanni Ferrero
MaRDI profile type: Publication
full work available at URL: a:1008311600271
OpenAlex ID: W2003994248
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description: scientific article; zbMATH DE number 1230698