<abstract xmlns="http://www.w3.org/1999/xhtml"><p>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.</p></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.

Rotation-Equivalence Classes of Binary Vectors

Institute of Computer Science and Mathematics, Faculty of Electrical Engineering and Information Technology, Slovak University of Technology in Bratislava, Ilkovičova 3, SK–812-19 Bratislava,

Tatra Mountains Mathematical Publications

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"Rotation-Equivalence Classes of Binary Vectors"}

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...

Rotation-Equivalence Classes of Binary Vectors

Published Online: Feb 25, 2017

Page range: 93 - 98

Received: Nov 18, 2016

DOI: https://doi.org/10.1515/tmmp-2016-0033

Keywords
rotational equivalence classes, binary vectors, binary vector rotation, rotational classes cardinality

© 2016 Otokar Grošek et al., published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Rotation-Equivalence Classes of Binary Vectors

Published Online: Feb 25, 2017

Page range: 93 - 98

Received: Nov 18, 2016

DOI: https://doi.org/10.1515/tmmp-2016-0033

Keywordsrotational equivalence classes, binary vectors, binary vector rotation, rotational classes cardinality

© 2016 Otokar Grošek et al., published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
rotational equivalence classes, binary vectors, binary vector rotation, rotational classes cardinality