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.

New results on modular Golomb rulers, optical orthogonal codes and related structures / Buratti, M.; Stinson, D. R.. - In: ARS MATHEMATICA CONTEMPORANEA. - ISSN 1855-3966. - 20:1(2020), pp. 1-27. [10.26493/1855-3974.2374.9FF]

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

Buratti M.;
2020

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.
2020
Difference family; Golomb ruler; Optical orthogonal code
01 Pubblicazione su rivista::01a Articolo in rivista
New results on modular Golomb rulers, optical orthogonal codes and related structures / Buratti, M.; Stinson, D. R.. - In: ARS MATHEMATICA CONTEMPORANEA. - ISSN 1855-3966. - 20:1(2020), pp. 1-27. [10.26493/1855-3974.2374.9FF]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1654640
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