this is for holding javascript data
Michela Ceria edited bits3.tex
over 7 years ago
Commit id: ea83aed84bbcc68c8a2579a155821e855226de55
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index ed48096..e36aa49 100644
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We notice the following facts:
\begin{itemize}
\item performing the algorithm (a finite number of times) we get again the initial vector $(1,0,1)$
\item
only performing the algorithm above, we find all the strings of three bits with at least a nonzero entry.
%only the numbers $1,2,3,4,5,6,7$ can be written using three bits not all zero and, performing the algorithm, we found all these numbers.
This is not true in general. The feedback polynomials for which this property holds is called \emph{primitive}.
\end{itemize}
In other words
\begin{Definition}\label{Primitive}
We call primitive a polynomial $f$ of degree $n$ that, used as feedback polynomials of a LFSR, can generate all the
$n$-tuples of bits with at least one nonzero entry.
\end{Definition}
\begin{Example}
We see now an example of non-primitive polynomial. Let us consider $f=x^3+1$ and we start again from $(1,0,1)$, and we perform the algorithm