Sidon Sequences and Doubly Periodic Two-Dimensional Synchronization Patterns

TL;DR

This paper explores the relationship between Sidon sequences and two-dimensional synchronization patterns, providing conditions for transformation and introducing a new construction method for Sidon sequences over specific alphabets.

Contribution

It offers new sufficient conditions for transforming 2D synchronization patterns into Sidon sequences and presents a novel construction method for Sidon sequences over prime power alphabets.

Findings

Established conditions for pattern-to-sequence transformation

Proposed a new Sidon sequence construction method

Applicable to alphabets of size q(q-1) where q is prime power

Abstract

Sidon sequences and their generalizations have found during the years and especially recently various applications in coding theory. One of the most important applications of these sequences is in the connection of synchronization patterns. A few constructions of two-dimensional synchronization patterns are based on these sequences. In this paper we present sufficient conditions that a two-dimensional synchronization pattern can be transformed into a Sidon sequence. We also present a new construction for Sidon sequences over an alphabet of size q(q-1), where q is a power of a prime.