Almost perfect binary functions

The almost perfect binary sequences have been defined in [6] as (−1, +1)-periodic sequences such that all their out-of-phase autocorrelation coefficients are zero except one. In the preceding paper, the study of the almost perfect binary sequences is done by means of the ringF2[X]/(Xn−1). Here, the arithmetic of cyclotomic fields enables us to solve open problems and questions like: structure and existence of these sequences.