Reducing the Computation of Linear Complexities of Periodic Sequences over $GF(p^m)$
<|reference_start|>Reducing the Computation of Linear Complexities of Periodic Sequences over $GF(p^m)$: The linear complexity of a periodic sequence over $GF(p^m)$ plays an important role in cryptography and communication [12]. In this correspondence, we prove a result which reduces the computation of the linear complexity and minimal connection polynomial of a period $un$ sequence over $GF(p^m)$ to the computation of the linear complexities and minimal connection polynomials of $u$ period $n$ sequences. The conditions $u|p^m-1$ and   $\gcd(n,p^m-1)=1$ are required for the result to hold. Some applications of this reduction in fast algorithms to determine the linear complexities and minimal connection polynomials of sequences over $GF(p^m)$ are presented.<|reference_end|>
@article{chen2006reducing,
    title={Reducing the Computation of Linear Complexities of Periodic Sequences
  over $GF(p^m)$},
    author={Hao Chen},
    journal={arXiv preprint arXiv:cs/0607104},
    year={2006},
    archivePrefix={arXiv},
    eprint={cs/0607104},
    primaryClass={cs.CR cs.IT math.IT}
}