Linear Shift-Register Synthesis for Multiple Sequences of Varying Length

Details Linear Shift-Register Synthesis for Multiple Sequences of Varying Length Linear Shift-Register Synthesis for Multiple Sequences of Varying Length

2006-05-09

arxiv.org/abs/cs/0605044v1

Computer Science

Information Theory

Scientific paper

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.

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