Combinatorial Designs Derived from Costas Arrays

Tuvi Etzion
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Tuvi Etzion: Computer Science Department, Technion

A chapter in Sequences, 1990, pp 208-227 from Springer

Abstract: Abstract A Costas array is an n×n 0-1 permutation matrix such that all the $$\left[ {\begin{array}{*{20}{c}}n \\2\end{array}} \right]$$ vectors connecting two ones in the matrix are distinct. Symmetry and periodicity have an important role in the known constructions for Costas arrays. We prove that some structures of symmetric (or periodic) Costas arrays are not possible, or exist for a limited number of cases. Using Costas arrays we can obtain other arrays which are symmetric and have 4-valued autocorrelation function. Finally, we give some constructions for plane-filling with Costas arrays, i.e., an n×n array with n symbols such that each symbol defines a Costas array.

Keywords: Permutation Matrix; Primitive Element; Primitive Root; Combinatorial Design; Bent Function (search for similar items in EconPapers)
Date: 1990
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4612-3352-7_16

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DOI: 10.1007/978-1-4612-3352-7_16

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