Abstract: An infinite family of Boolean polynomials which correspond to the discrete average maps, defined in [2], is constructed. Each member of the family is found to be balanced. A recursive formula, which computes from is provided. |
Keywords and phrases: Boolean polynomial, space of rhythms, discrete average, Boolean average, balanced polynomial.
Received: August 14, 2021; Accepted: September 16, 2021; Published: November 10, 2021
How to cite this article: Fumio Hazama, Boolean polynomial expression of the discrete average on the space of rhythms, JP Journal of Algebra, Number Theory and Applications 52(2) (2021), 179-242. DOI: 10.17654/NT052020179
This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License
References:
[1] T. W. Cusick and P. Stănică, Cryptographic Boolean Functions and Applications, Elsevier/Academic Press, Amsterdam, The Netherlands, 2009. [2] F. Hazama, Iterative method of construction for smooth rhythms, Journal of Mathematics and Music (2021), On-Line-First, pp. 1-20. https://doi.org/10.1080/17459737.2021.1924303. [3] F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-correcting Codes, Elsevier/North Holland, Amsterdam, the Netherlands, 1977. [4] J. E. Whitesitt, Boolean Algebra and its Application, Dover Books on Computer Science, 2010.
|