Asymptotic study of the maximum number of edges in a uniform hypergraph with one forbidden intersection

The object of this research is the quantity defined as the maximum number of edges in a -uniform hypergraph possessing the property that no two edges intersect in vertices. The case when and as , and , are fixed constants is considered in full detail. In the case when the asymptotic accuracy of the Frankl-Wilson upper estimate is established; in the case when new lower estimates for the quantity are proposed. These new estimates are employed to derive upper estimates for the quantity , which is widely used in coding theory and is defined as the maximum number of bit strings of length and weight having Hamming distance at least from one another. Bibliography: 38 titles.