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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Existence of symmetric skew balanced starters for odd prime powers


Authors: Ding Zhu Du and F. K. Hwang
Journal: Proc. Amer. Math. Soc. 104 (1988), 660-667
MSC: Primary 05B10
DOI: https://doi.org/10.1090/S0002-9939-1988-0962844-1
MathSciNet review: 962844
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Abstract: Strong starters and skew starters have been widely used in various combinatorial designs. In particular skew balanced starters and symmetric skew balanced starters are crucially used in the construction of completely balanced Howell rotations. Let $ n = {2^m}k + 1$ be an odd prime power where $ m \geq 2$ and $ k$ is an odd number. The existence of symmetric skew balanced starters for $ GF(n)$ has been proved for $ m \geq 2$ and $ k \ne 1,3,9$. In this paper, we present a new approach which gives a uniform proof of the existence of symmetric skew balanced starters for all $ m \geq 2$ and $ k \geq 3$.


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DOI: https://doi.org/10.1090/S0002-9939-1988-0962844-1
Article copyright: © Copyright 1988 American Mathematical Society