New results on modular Golomb rulers, optical orthogonal codes and related structures - Buratti, Marco (Ars mathematica contemporanea, 2021)
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.
Keywords: diferenčna družina; difference family; Golomb ruler; Golombovo ravnilo; optical orthogonal code; optična ortogonalna koda