Infinite families of 2-designs from a class of linear codes related to Dembowski-Ostrom functions
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Due to their important applications to coding theory, cryptography, communications and statistics, combinatorial t-designs have been attracted lots of research interest for decades. The interplay between coding theory and t-designs has on going for many years. As we all known, t-designs can be used to derive linear codes over any finite field, as well as 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.
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