2020/07/03 by Buratti, Marco, Stinson, Douglas R.
#05B10 #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2007.01908
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.