A generalization of the binary Preparata code

AbstractA classical binary Preparata code P2(m) is a nonlinear (2m+1,22(2m-1-m),6)-code, where m is odd. It has a linear representation over the ring Z4 [Hammons et al., The Z4-linearity of Kerdock, Preparata, Goethals and related codes, IEEE Trans. Inform. Theory 40(2) (1994) 301–319]. Here for any q=2l>2 and any m such that (m,q-1)=1 a nonlinear code Pq(m) over the field F=GF(q) with parameters (q(Δ+1),q2(Δ-m),d⩾3q), where Δ=(qm-1)/(q-1), is constructed. If d=3q this set of parameters generalizes that of P2(m). The equality d=3q is established in the following cases: (1) for a series of initial admissible values q and m such that qm