Infinite families of t-designs from the binomial x4+x3 over GF(2n).

Combinatorial t-designs have nice applications in coding theory, finite geometries and engineering areas. t-designs can be constructed from image sets of a fixed size of some special polynomials. This paper constructs t-designs from the quadratic polynomial x 4 + x 3 over GF (2 n) and determine their parameters. We yield 2- 2 n , 3 · 2 n - 2 , 3 · 2 n - 2 3 · 2 n - 2 - 1 designs for n even and 3- 2 n , 2 n - 1 , 2 n - 1 2 n - 2 - 1 designs for n odd. [ABSTRACT FROM AUTHOR]