Mutually orthogonal rectangular gerechte designs

作者：Bremigan Ralph; Lorch John^*

来源：Linear Algebra and Its Applications, 2016, 497: 44-61.

DOI：10.1016/j.laa.2016.02.017

• Gerechte design
• Orthogonality
• Toeplitz matrix

Let q be a prime power and r, s,m,n positive integers. We construct families of mutually orthogonal gerechte designs of order q(r+s) with rectangular regions of size q(r) x 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 mxn. The construction is linear-algebraic; surrounding theory employs companion matrices and Toeplitz matrices over finite fields.

• 出版日期2016-5-15