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

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 solv...

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Bibliographic Details
Published in:Designs, codes, and cryptography Vol. 83; no. 2; pp. 283 - 305
Main Authors: Kuijper, M., Pinto, R.
Format: Journal Article
Language:English
Published: New York Springer US 01.05.2017
Springer Nature B.V
Subjects:
Circuits
Coding and Information Theory
Computer Science
Cryptology
Data Structures and Information Theory
Discrete Mathematics in Computer Science
Feedback
Information and Communication
Iterative algorithms
Parameterization
Registers
Shift registers
Polynomial modules
Minimal basis
Parametrization
Sequences
16P10
Shift registers
Iterative algorithms
94A55
ISSN:0925-1022, 1573-7586
Online Access:Get full text
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Summary: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 ) .
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ISSN:0925-1022
1573-7586
DOI:10.1007/s10623-016-0226-3