On cyclic Goppa codes and sequence designs

Berlekamp and Moreno (1973) and Tzeng and Zimmerman (1975) proved that extended binary Goppa codes are cyclic codes. They have parameters (2^m+1, 2m, 6) and the Goppa polynomial is a quadratic. In this paper we use the result in Berlekamp and Moreno to introduce a sequence design having length 2^m+1 and correlation ⩽2√(2^m). The family size is 2^m-1 and the linear span is 2m. For the correlation, we use the computation of the dual distance of the Goppa codes using Bombieri