An iterative algorithm for parametrization of shortest length shift registers over finite rings

Details An iterative algorithm for parametrization of shortest length shift registers over finite rings An iterative algorithm for parametrization of shortest length shift registers over finite rings

2012-01-28

arxiv.org/abs/1201.5921v1

Computer Science

Information Theory

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Scientific paper

The construction of shortest feedback shift registers for a finite sequence S_1,...,S_N is considered over the finite ring Z_{p^r}. A novel algorithm is presented that yields a parametrization of all shortest feedback shift registers for the sequence of numbers S_1,...,S_N, thus solving an open problem in the literature. The algorithm iteratively processes each number, starting with S_1, and constructs at each step a particular type of minimal Gr\"obner basis. The construction involves a simple update rule at each step which leads to computational efficiency. It is shown that the algorithm simultaneously computes a similar parametrization for the reciprocal sequence S_N,...,S_1.

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