this is for holding javascript data
Massimiliano Sala edited bits3.tex
over 7 years ago
Commit id: bdb7f2a62e48286fa2fdb28ccadcb0c2b23b8de7
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producing $n$-bit vectors and such that any initial state is got again after
a finite number of iterations.\\
Fact (\ref{fatc-b}) is more difficult to generalize. If we want an LFSR that can start from any initial nonzero vector and obtain all other nonzero vectors, then we must use very special polynomials, called \emph{primitive} polynomials.
In other words %
\begin{Definition}\label{Primitive}
We call primitive
a any polynomial
$f$ $f\in \FF_2[x]$ of degree $n$ that, used as feedback polynomials of a LFSR, can generate all the
non-zero
$n$-tuples of
bits with at least one nonzero entry,i.e. bits,i.e. all the $n$-tuples but
$(0,0,0,...,0,0)$. $(0,0,0,...,0,0)$, using as initial
state any of these.
\end{Definition}