Group divisible designs with large block sizes
type: Item
instance of: scholarly article
title: Group divisible designs with large block sizes
zbMATH Open document ID: 1400.05034
author: Lijun Ji
published in: Designs, Codes and Cryptography
publication date: 2018-09-06T00:00:00Z
review text: In this paper, the author showed that there is a \((k,\lambda_k)\)-GDD, group divisible design, of type \((q^{l+1}-q^l)^{(q^{n-l}-1)/(q-1)}\), for any prime power \(q\) and any integers \(k\), \(n\) with \(3\leq k \leq n\), where \(\lambda_k=\frac{\prod_{i=3}^{k-1}(q^n-q^{l+i-1})}{(k-2)!}\) and \(k+l\leq n+1\). The author generalized the \textit{C.-D. Lee} et al.'s method [ibid. 86, No. 6, 1281--1293 (2018; Zbl 1387.05024)] and used counting principles to construct such GDD. Moreover, the author showed that the conjecture given by C.-D. Lee at al. [loc. cit.] holds. It is a special case of the method given in this paper, for \(q=2\) and \(l=1\).
Mathematics Subject Classification ID: 05B05
zbMATH DE Number: 6933689
zbMATH Keywords: group divisible designs
zbMATH Keywords: finite field
zbMATH Keywords: linearly independent
reviewed by: Andrea Švob
MaRDI profile type: Publication
full work available at URL: s10623-017-0448-z
OpenAlex ID: W2771212054
cites work: Constructions of strictly \(m\)-cyclic and semi-cyclic \(H(m,n,4,3)\)
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DOI: 10.1007/S10623-017-0448-Z
description: scientific article; zbMATH DE number 6933689