Binary m-sequences with three-valued crosscorrelation: a proof of Welch´s conjecture

We prove the long-standing conjecture of Welch stating that for odd n=2m+1, the power function x^d with d=2^m+3 is maximally nonlinear on GF(2ⁿ) or, in other terms, that the crosscorrelation function between a binary maximum-length linear shift register sequence of degree n and a decimation of that sequence by 2^m+3 takes on precisely the three values -1, -1±2^m+1