Linear Shift-Register Synthesis for Multiple Sequences of Varying Length
<|reference_start|>Linear Shift-Register Synthesis for Multiple Sequences of Varying Length: The problem of finding the shortest linear shift-register capable of generating t finite length sequences over some field F is considered. A similar problem was already addressed by Feng and Tzeng. They presented an iterative algorithm for solving this multi-sequence shift-register synthesis problem, which can be considered as generalization of the well known Berlekamp-Massey algorithm. The Feng-Tzeng algorithm works indeed, if all t sequences have the same length. This paper focuses on multi-sequence shift-register synthesis for generating sequences of varying length. It is exposed, that the Feng-Tzeng algorithm does not always give the correct solution in this case. A modified algorithm is proposed and formally proved, which overcomes this problem.<|reference_end|>
@article{schmidt2006linear,
    title={Linear Shift-Register Synthesis for Multiple Sequences of Varying Length},
    author={Georg Schmidt, and Vladimir R. Sidorenko},
    journal={arXiv preprint arXiv:cs/0605044},
    year={2006},
    archivePrefix={arXiv},
    eprint={cs/0605044},
    primaryClass={cs.IT math.IT}
}