New Results on Modular Golomb Rulers, Optical Orthogonal Codes and Related Structures

2020/07/03 by Marco Buratti, Douglas R. Stinson, Buratti, Marco +1
Mathematics · #05B10 #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05B10

paper · pdf · doi:10.48550/arxiv.2007.01908

Typos in Corollary 3.4 were corrected

arxiv created 2020/10/11 · arxiv updated 2020/10/13

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.

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