Infinite families of 2-designs from a class of non-binary Kasami cyclic codes
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Combinatorial t-designs have been an important research subject for many years, as they have wide applications in coding theory, cryptography, communications and statistics. The interplay between coding theory and t-designs has been attracted a lot of attention for both directions. It is well known that a linear code over any finite field can be derived from the incidence matrix of a t-design, meanwhile, that the supports of all codewords with a fixed weight in a code also may hold a t-design. In this paper, by determining the weight distribution of a class of linear codes derived from non-binary Kasami cyclic codes, we obtain infinite families of 2-designs from the supports of all codewords with a fixed weight in these codes, and calculate their parameters explicitly.
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