ResumenA es un conjunto de Sidon en un grupo conmutativo G notado aditivamente si el número de representaciones de todo elemento no identidad de G como diferencia de dos elementos de A es a lo sumo 1. Una secuencia sonar m × n es una función f : {1, . . . , n} → {1, . . . , m} tal que su grafo asociado G f := {(x, f (x)) : 1 ≤ x ≤ n} es un conjunto de Sidon en el grupo Z × Z. Si G(m) denota el máximo entero positivo n tal que existe una secuencia sonar m × n, utilizando el concepto de energía aditiva y algunas de sus propiedades elementales. En este trabajo se prueba que G(m) ≤ m + 3,78m 2/3 + 4,76m 1/3 + 2. Además, utilizando la construcción de conjuntos de Sidon tipo Bose en Z q 2 −1 se construyen secuencias sonar (q − 1) × q, para toda potencia prima q.Palabras Clave: Conjuntos de Sidon, secuencias sonar, energía aditiva. AbstractA 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 × 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 × Z. If G(m) denotes the maximum positive integer such that there exists an m × n sonar sequence, using additive energy and some of its properties. In this paper, we show that G(m) ≤ m + 3,78m2/3 + 4,76m 1/3 + 2. Furthermore, using the construction of Sidon sets type Bose in Z q 2 −1 we construct (q − 1) × q sonar sequences for all prime power q. SECUEN Rigo Jul Carlos A RecibiResumen A es un conjunto el número de represen de dos elementos de f : {1, . . . , n} → {1, . es un conjunto de Sido n tal que existe una s y algunas de sus pro m + 3,78m 2/3 + 4,76m tipo Bose en Z q 2 −1 se q. Palabras Clave: Con AbstractA is a Sidon set in of each non-identity e 1. An m × n sonar se associated graph G f : If G(m) denotes the m sequence, using additiv G(m) ≤ m + 3,78m 2/3
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