An iterative algorithm for parametrization of shortest length linear shift registers over finite chain rings - Kuijper, M.; Pinto, R. (Designs, codes, and cryptography, 2017)
The construction of shortest feedback shift registers for a finite sequence S 1 , … , S N is considered over finite chain rings, such as 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 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 reverse sequence S N , … , S 1 . The complexity order of the algorithm is shown to be O ( r N 2 ) .