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On the Complexity of the Verification of the Costas Property

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3 Author(s)
Barker, L. ; Xilinx Design Services, Xilinx Ireland, Dublin ; Drakakis, K. ; Rickard, S.

In this paper, we show that in order to ascertain whether a permutation has the Costas property, only a restricted subset among the totality of pairs of entries in the same row of the difference triangle needs to be checked, and we explicitly describe such a subset. This represents a further refinement on the definition of a Costas permutation. This observation can be used to speed up algorithms that exhaustively search for Costas permutations. Asymptotically, the savings approaches 43% for large orders when compared with the previous standard efficient method.

Published in:

Proceedings of the IEEE  (Volume:97 ,  Issue: 3 )