almost perfect sequences

Definitions

Let n be a positive integer. A binary almost perfect sequences of length n is a mapping f from the cyclic group Z/nZ into {-1,+1} whose the autocorrelation values are 0 except two times.

fxf(0) = n,   fxf(n/2)=4-n
The length of a such sequence is a multiple of 4 but one conjectures that such sequence exists if and only if n = 2 (q+1) where q is a power of a prime.

code

One can use the finite field GF(q^2) to construct a sequence of length 2(q+1). An implantation of the methode of Bradley and Pott is given by the three files below. Enjoy !


Philippe Langevin, Last modification, june 2017.