Mutually orthogonal rectangular gerechte designs

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• 作者：Ralph Bremigan ; John Lorch ; ^{jlorch@bsu.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：05B15 ; 15B05
• 刊名：Linear Algebra and its Applications
• 出版年：2016
• 出版时间：15 May 2016
• 年：2016
• 卷：497
• 期：Complete
• 页码：44-61
• 全文大小：405 K

文摘

Let q   be a prime power and r,s,m,n$r,s,m,n$ positive integers. We construct families of mutually orthogonal gerechte designs of order q^r+s$q^{r+s}$ with rectangular regions of size q^r×q^s$q^r\times q^s$. This leads to a lower bound on the size of a family of mutually orthogonal gerechte designs of order mn   with rectangular regions of size m×n$m\times n$. The construction is linear-algebraic; surrounding theory employs companion matrices and Toeplitz matrices over finite fields.