Rotation-Equivalence Classes of Binary Vectors

Otokar Grošek; Viliam Hromada

doi:10.1515/tmmp-2016-0033

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Rotation-Equivalence Classes of Binary Vectors

Tatra Mountains Mathematical Publications

Volume 67 (2016): Issue 1 (September 2016)

By: Otokar Grošek and Viliam Hromada

Open Access

|Feb 2017

Abstract

In this paper we study equivalence classes of binary vectors with regards to their rotation by using an algebraic approach based on the theory of linear feedback shift registers. We state the necessary and sufficient condition for existence of an equivalence class with given cardinality and provide two formulas. The first represents the sharp distribution of cardinalities for given length and Hamming weight of binary vectors and the second enables us to determine the number of different classes with the same cardinality.

References

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Articles in this issue

DOI: https://doi.org/10.1515/tmmp-2016-0033 | Journal eISSN: 1338-9750 | Journal ISSN: 1210-3195

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Language: English

Page range: 93 - 98

Submitted on: Nov 18, 2016

Published on: Feb 25, 2017

Published by: Slovak Academy of Sciences, Mathematical Institute

In partnership with: Paradigm Publishing Services

Publication frequency: 1 issue per year

Keywords:

rotational equivalence classes,

binary vectors,

binary vector rotation,

rotational classes cardinality

Related subjects:

Mathematics,

General mathematics

© 2017 Otokar Grošek, Viliam Hromada, published by Slovak Academy of Sciences, Mathematical Institute
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Volume 67 (2016): Issue 1 (September 2016)