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, 3.2n-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.