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arXiv · 2611.00098

Comments on "Multidimensional Costas Arrays and Their Periodicity"

Shiv Munagala
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Abstract

Rubio and Torres conjectured that a multidimensional Costas array, defined by a bijection between two boxes of integer points whose domain has at least as many dimensions as its image, can stay Costas in every window of its periodic extension only if its order is a power of two fixed by the dimension of the domain. We give a four-dimensional periodic Costas array of order $6$, with a two-dimensional domain and a two-dimensional image, so the conjecture is false. The verification reduces to $36$ windows. It has been confirmed by computer and in the Lean proof assistant. The array also meets with equality the pigeonhole bound that Rubio and Torres use for their non-existence results, so that bound is tight.

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Shiv Munagala. 2026-10-25. Comments on "Multidimensional Costas Arrays and Their Periodicity". https://arxiv.org/abs/2611.00098

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