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<p>In this paper, we apply the theory of vanishing sums to study cyclic Butson matrices. First, we show that there is essentially “only one” Butson matrix over a group of prime order, which was previously not known. We then find a necessary condition for the existence of cyclic Butson matrices of order 2<i>p</i> where <i>p</i> is prime. For small <i>p</i>, we demonstrate how we might be able to determine all cyclic Butson matrices of order 2<i>p</i>. Specifically, we determine all cyclic Butson matrices of order 6.</p>

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On vanishing sums and cyclic Butson matrices

  • 期刊论文

  • 发表日期：

    2025年8月26日

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  • Ka Hin Leung,
  • Jun Heng Edmil Chue,
  • Meng Zhao

摘要

In this paper, we apply the theory of vanishing sums to study cyclic Butson matrices. First, we show that there is essentially “only one” Butson matrix over a group of prime order, which was previously not known. We then find a necessary condition for the existence of cyclic Butson matrices of order 2p where p is prime. For small p, we demonstrate how we might be able to determine all cyclic Butson matrices of order 2p. Specifically, we determine all cyclic Butson matrices of order 6.