Infinite Families of 2-Designs from a Class of Linear Codes Related to Dembowski-Ostrom Functions.

Due to their important applications to coding theory, cryptography, communications and statistics, combinatorial t -designs have attracted lots of research interest for decades. The interplay between coding theory and t -designs started many years ago. It is generally known that t -designs can be used to derive linear codes over any finite field, and that the supports of all codewords with a fixed weight in a code also may hold a t -design. In this paper, we first construct a class of linear codes from cyclic codes related to Dembowski-Ostrom functions. By using exponential sums, we then determine the weight distribution of the linear codes. Finally, we obtain infinite families of 2 -designs from the supports of all codewords with a fixed weight in these codes. Furthermore, the parameters of 2 -designs are calculated explicitly. [ABSTRACT FROM AUTHOR]