1 research outputs found
Infinite families of -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 -designs have been attracted
lots of research interest for decades. The interplay between coding theory and
-designs has on going for many years. As we all known, -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 -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 -designs from the supports of all codewords with a fixed weight in these
codes. Furthermore, the parameters of -designs are calculated explicitly.Comment: arXiv admin note: substantial text overlap with arXiv:1912.04745;
text overlap with arXiv:1903.07459, arXiv:1904.0424