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

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3 Author(s)
Canteaut, A. ; Inst. Nat. de Recherche en Inf. et Autom., Le Chesnay, France ; Charpin, P. ; Dobbertin, H.

We prove the long-standing conjecture of Welch stating that for odd n=2m+1, the power function xd with d=2m+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 2m+3 takes on precisely the three values -1, -1±2m+1

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Information Theory, IEEE Transactions on  (Volume:46 ,  Issue: 1 )