New results on modular Golomb rulers, optical orthogonal codes and related structures
Keywords:Golomb ruler, optical orthogonal code, difference family
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.
Articles in this journal are published under Creative Commons Attribution 4.0 International License