Resumo

OSORIO, Rigo Julián; RUIZ, Diego Fernando; TRUJILLO, Carlos Alberto  e  URBANO, Cristhian Leonardo. Sonar Sequences and Sidon Sets. rev. cienc. [online]. 2014, vol.18, n.1, pp.33-42. ISSN 0121-1935.

A is a Sidon set in an additive commutative group G if the number of representations of each non-identity element in G, as a difference of two elements in A is at most 1. An m x n sonar sequence is a function f : {1, .. . , n} → {1, .. . , m} such that its associated graph G f := {(x, f (x)) : 1 ≤x ≤ n} is a Sidon set in the group Z x Z. If G(m) denotes the maximum positive integer such that there exists an m x n sonar sequence, using additive energy and some of its properties. In this paper, we show that G(m) ≤ m + 3,78m2/3 + 4,76m1/3 + 2. Furthermore, using the construction of Sidon sets type Bose in Zq2 -1 we construct (q - 1) x q sonar sequences for all prime power q

Palavras-chave : Sidon sets; sonar sequences; additive energy.

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