On the Duals of Binary Hyper-Kloosterman Codes

Abstract. Binary hyper-Kloosterman codes C(r,m) of length (2r − 1) are a quasi-cyclic generalization of the dual of the Melas code of length 2r − 1. In this note the duals C(r,m) i.e. a generalization of the Melas code C(r, 2) itself are studied. In particular, the minimum distance of C(r,m) for all r,m ≥ 2, the weight distribution of C(2, m) and C(2, m) for all m ≥ 2, and the weight distribution of C(r, 3) and C(r, 3) for all r ≥ 2 is obtained.