模Golomb尺、光学正交码及相关结构的新成果

Ars Math. Contemp. Pub Date : 2020-07-03 DOI:10.26493/1855-3974.2374.9ff

M. Buratti, Douglas R Stinson

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引用次数: 6

摘要

本文证明了模Golomb标尺的存在性和不存在性的新结果。我们完全确定了阶为$k$的模Golomb标尺对所有$k\leq 11$存在，并给出了对所有$k \geq 3$存在的一般结果。我们还得到了无限类模Golomb标尺及其相关结构如差分填充、光学正交码、循环斯坦纳系统和相对差分族的不存在性的新结果。

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New results on modular Golomb rulers, optical orthogonal codes and related structures

We prove new existence and nonexistence results for modular Golomb rulers in this paper. We completely determine which modular Golomb rulers of order $k$ exist, for all $k\leq 11$, and we present a general existence result that holds for all $k \geq 3$. We also derive new nonexistence results for infinite classes of modular Golomb rulers and related structures such as difference packings, optical orthogonal codes, cyclic Steiner systems and relative difference families.

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Ars Math. Contemp.

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