Near-Optimal <italic>g</italic>-Golomb Rulers

Abstract

A set of positive integers A is called a $g$ -Golomb ruler if the difference between two distinct elements of A is repeated up to $g$ times. This definition is a generalization of the Golomb ruler $(g = 1)$ . In this paper, we obtain new constructions for $g$ -Golomb rulers from Golomb rulers, using these constructions we find some suboptimal 2 and 3-Golomb rulers with up to 124 marks and we prove two theorems related to extremal functions associated with this sets improving already known results.

Keywords

• Golomb rulers
• g-Golomb rulers%22%2C%22default_operator%22%3A%22AND%22%7D%7D%7D"> <italic xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">g</italic>-Golomb rulers
• intermodulation interference