Permutation Equivalence of Quartic 2-Rotation Symmetric Boolean Functions

A Boolean function is considered to be rotation symmetric if it is invariant under cyclic rotation, ρ, of the input variables, and is considered to be 2-rotation symmetric if it is invariant under ρ2. A 2−rotation symmetric function is considered to be 2−monomial rotation symmetric (2-MRS) if the function is generated by applications of ρ2 to a single monomial term. This thesis focuses on the study of mixed form 2 (mf2) quartic 2-MRS functions. These functions are generated from the monomial x1xaxbxc, in 2n variables, denoted 2-(1,a,b,c)2n, with exactly one of a,b or c odd. We give a general method to determine when any two mf2 functions are equivalent by a permutation of the variables. This uses the theory of affine equivalence of quadratic MRS functions in n variables, which was studied in [13]. Additionally, we show how to calculate the number of equivalence classes, and give an explicit formula in the case when the number of variables, n = pk,pq or 2k, where p,q are odd primes.

Grantor dc:publisher

State University of New York at Buffalo

Year dc:date.issued

2018

Author dc:creator

• Dougan, Kelly

Contributors dc:contributor

• Cusick, Thomas
• Mathematics

• mathematics

Statement dc:rights

• Users of works found in University at Buffalo Institutional Repository (UBIR) are responsible for identifying and contacting the copyright owner for permission to reuse. University at Buffalo Libraries do not manage rights for copyright-protected works and cannot assist with permissions.
• Copyright retained by author.

Language dc:language

eng

Handle dc:identifier

http://hdl.handle.net/10477/78055

OAI record oai:identifier

https://ubir.buffalo.edu/oai/request?verb=GetRecord&metadataPrefix=qdc&identifier=oai%3Aubir.buffalo.edu%3A10477%2F78055