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\input zb-ioport
\iteman{io-port 00404213}
\itemau{Komo, John J.; Lam, Maurice S.}
\itemti{Primitive polynomials and $m$-sequences over GF($q\sp m$).}
\itemso{IEEE Trans. Inf. Theory 39, No.2, 643-647 (1993).}
\itemab
Expressions for obtaining $m$-sequences over $\text{GF}(q\sp m)$ and the primitive polynomials that generate them, in terms of $m$-sequences over $\text{GF}(q)$ and their primitive polynomials, have been developed. Expressions for the primitive polynomials in $\text{GF}[q\sp m,x]$, and their corresponding $m$-sequences, which are the remaining factors of the primitive polynomial in $\text{GF}[q,x]$ are also obtained. In addition, the $m$-sequences and the primitive polynomials that generate them are derived for any decimation of the original $m$-sequence over $\text{GF}(q\sp m)$. Finally, the corresponding $m$-sequences and primitive polynomials are obtained for any change of basis for expressing $\text{GF}(q\sp m)$ over $\text{GF}(q)$.
\itemrv{~}
\itemcc{}
\itemut{trace dual basis; shift factor; finite fields; $m$-sequences; primitive polynomials; decimation}
\itemli{doi:10.1109/18.212297}
\end