New results on modular Golomb rulers, optical orthogonal codes and related structures

Authors

DOI:

https://doi.org/10.26493/1855-3974.2374.9ff

Keywords:

Golomb ruler, optical orthogonal code, difference family

Abstract

We prove new existence and nonexistence results for modular Golomb rulers in this paper. We completely determine which modular Golomb rulers of order k exist, for all k ≤ 11, and we present a general existence result that holds for all k ≥ 3. We also derive new nonexistence results for infinite classes of modular Golomb rulers and related structures such as difference packings, optical orthogonal codes, cyclic Steiner systems and relative difference families.

Published

2020-11-26

Issue

Section

Articles