7 citations · 20 across the 12 of their papers we have counts for
6 papers · 1 filter
On the Fourier Spectra of the Infinite Families of Quadratic APN Functions
Carl Bracken, Zhengbang Zha
It is well known that a quadratic function defined on a finite field of odd degree is almost bent (AB) if and only if it is almost perfect nonlinear (APN). For the even degree case…
A Few More Quadratic APN Functions
Carl Bracken, Eimear Byrne, Nadya Markin +1
We present two infinite families of APN functions where the degree of the field is divisible by 3 but not 9. Our families contain two already known families as special cases. We al…
Counting the Number of Site Swap Juggling Patterns with Respect to Particular Ceilings
Carl Bracken
Site swap is a mathematical notation used by jugglers to communicate, create and study complex juggling patterns. Determining the number of possible site swap juggling patterns wit…
Pseudo Quasi-3 Designs and their Applications to Coding Theory
Carl Bracken
We define a pseudo quasi-3 design as a symmetric design with the property that the derived and residual designs with respect to at least one block are quasi-symmetric. Quasi-symmet…
Fourier Spectra of Binomial APN Functions
Carl Bracken, Eimear Byrne, Nadya Markin +1
In this paper we compute the Fourier spectra of some recently discovered binomial APN functions. One consequence of this is the determination of the nonlinearity of the functions,…
New Families of Triple Error Correcting Codes with BCH Parameters
Carl Bracken
Discovered by Bose, Chaudhuri and Hocquenghem, the BCH family of error correcting codes are one of the most studied families in coding theory. They are also among the best performi…