ENUMERATION AND CODING METHODS FOR A CLASS OF PERMUTATIONS AND REVERSIBLE LOGICAL GATES

Costas Karanikas, Nikolaos Atreas

DOI Number
10.2298/FUEE1802241K
First page
241
Last page
255

Abstract


We introduce a great variety of coding methods for boolean sparse invertible matrices and we use these methods to create a variety of bijections on the permutation group P(m) of the set {1,2,...,m}. Also, we propose methods for coding, enumerating and shuffling the set{0,...,2m−1}, i.e. the set of all m-bit binary arrays. Moreover we show that several well known reversible logic gates/circuits (on m-bit binary arrays) can be coded by sparse matrices.

Keywords

Permutations, Reversible Logical Gates.

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References


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