A classical combinatorial number theory problem is to determine the maximum size of a Sidon set {1,2,…,n}, where subset integers if all its pairwise sums are different. For this entry point into subject, combining two elementary proofs, we decrease gap between upper and lower bounds by 0.2% for infinitely many values n. We show that {1,2,…,n} at most n+0.998n1/4 n sufficiently large.

Sidon space is an important tool for constructing cyclic subspace codes. In this letter, we construct some spaces by using primitive elements and the roots of irreducible polynomials over finite fields. Let q be a prime power, k, m, n three positive integers $\rho= \lceil \frac{m}{2k}\rceil-1$, $\theta= \frac{n}{2m}\rceil-1$. Based on these union spaces, new codes with size $\frac{3(q^{n}-1)}{q...

in this paper we define ?-independent (a weak-version of independence), kronecker and dissociate sets on hypergroups and study their properties and relationships among them and some other thin sets such as independent and sidon sets. these sets have the lacunarity or thinness property and are very useful indeed. for example varopoulos used the kronecker sets to prove the malliavin theorem. in t...

In a note in this Journal [16 (1941), 212-215], Turan and I proved, among other results, the following : Let a l < a2 < . . . < a, < n be a sequence of positive integers such that the sums aj+a; are all different . Then x < n'1 +0(n1 ) . On the other hand, there exist such sequences with x >n1(2---e), for any e >0 . Recently I noticed that J . Singer, in his paper "A theorem in finite projectiv...