Given a binary sequence S, and integers f and d, return the decimation of S. This is the sequence containing elements S[f], S[f + d], S[f + 2d], ... where the indices in S are interpreted with wrap-around as integers between 1 and #S.
Decimation of the sequence S. Returns a new sequence containing the first t elements of S[f], S[f + d], S[f + 2d], ... where the indices in S are interpreted with wrap-around as integers between 1 and #S.
> K := GF(7); > C<D> := PrimitivePolynomial(K, 2); > C; D^2 + 6*D + 3In order to generate an LFSR sequence, we must first multiply this polynomial by a suitable constant so that the trailing coefficient becomes 1.
> C := C * Coefficient(C,0)^-1; > C; 5*D^2 + 2*D + 1We are now able to generate an LFSR sequence of length 72 - 1. The initial state can be anything other than [0, 0].
> t := LFSRSequence (C, [K| 1,1], 48); > t; [ 1, 1, 0, 2, 3, 5, 3, 4, 5, 5, 0, 3, 1, 4, 1, 6, 4, 4, 0, 1, 5, 6, 5, 2, 6, 6, 0, 5, 4, 2, 4, 3, 2, 2, 0, 4, 6, 3, 6, 1, 3, 3, 0, 6, 2, 1, 2, 5 ]We decimate the sequence by a value d having the property gcd(d, 48)=1.
> t := Decimation(t, 1, 5); > t; [ 1, 5, 0, 6, 5, 6, 4, 4, 3, 1, 0, 4, 1, 4, 5, 5, 2, 3, 0, 5, 3, 5, 1, 1, 6, 2, 0, 1, 2, 1, 3, 3, 4, 6, 0, 3, 6, 3, 2, 2, 5, 4, 0, 2, 4, 2, 6, 6 ] > B := BerlekampMassey(t); > B; 3*D^2 + 5*D + 1To get the corresponding primitive polynomial, we multiply by a constant to make it monic.
> B := B * Coefficient(B, 2)^-1; > B; D^2 + 4*D + 5 > IsPrimitive(B); true[Next][Prev] [_____] [Left] [Up] [Index] [Root]