gen () sage: fill = key = n = 20 sage: L = lfsr_sequence ( key, fill, 20 ) L sage: from _massey import berlekamp_massey sage: g = berlekamp_massey ( L ) g x^4 + x^3 + 1 sage: ( 1 ) / ( g. Sage: F = GF ( 2 ) l = F ( 1 ) o = F ( 0 ) sage: F = GF ( 2 ) S = LaurentSeriesRing ( F, 'x' ) x = S. OUTPUT: autocorrelation sequence of \(L\) L – a periodic sequence of elements of ZZ or GF(2) must have length \(p\) Timothy Brock (): added lfsr_autocorrelation and Timothy Brock (2005-11): added lfsr_sequence with code modified from This is the function of the Berlekamp-Massey algorithm, implemented However, this sequence of period 15 canīe “cracked” (i.e., a procedure to reproduce \(g(x)\)) by knowing only 8 terms! The sequence of \(0,1\)’s is periodic with period \(P=2^4-1=15\) and satisfies
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