Rotation-Equivalence Classes of Binary Vectors
| Autor: | Viliam Hromada, Otokar Grošek |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
Discrete mathematics
Distribution (number theory) General Mathematics 010102 general mathematics Binary number 02 engineering and technology 01 natural sciences Boundary-value analysis Combinatorics Cardinality 0202 electrical engineering electronic engineering information engineering 020201 artificial intelligence & image processing 0101 mathematics Algebraic number Hamming weight Rotation (mathematics) Equivalence class Mathematics |
| Zdroj: | Tatra Mountains Mathematical Publications. 67:93-98 |
| ISSN: | 1210-3195 |
| DOI: | 10.1515/tmmp-2016-0033 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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