A review of the available construction methods for Golomb rulers

Konstantinos Drakakis

doi:10.3934/amc.2009.3.235

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2009, Volume 3, Issue 3: 235-250. Doi: 10.3934/amc.2009.3.235

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A review of the available construction methods for Golomb rulers

Konstantinos Drakakis^1,

1.
UCD CASL, University College Dublin, Belfield, Dublin 4

Received: January 2009

Revised: July 2009

Published: August 2009

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Abstract

We collect the main construction methods for Golomb rulers available in the literature along with their proofs. In particular, we demonstrate that the Bose-Chowla method yields Golomb rulers that appear as the main diagonal of a special subfamily of Golomb Costas arrays. We also show that Golomb rulers can be composed to yield longer Golomb rulers.

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Mathematics Subject Classification: Primary: 05B10, 11B50; Secondary: 51E15, 05B20.

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