7 citations · 20 across the 5 of their papers we have counts for
5 papers
Quadratic Binomial APN Functions and Absolutely Irreducible Polynomials
E. Byrne, G. McGuire
We show that many quadratic binomial functions on a finite field of characteristic 2 are not APN infinitely often. This is of interest in the light of recent discoveries of new fam…
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…
Ring geometries, Two-Weight Codes and Strongly Regular Graphs
E. Byrne, M. Greferath, T. Honold
It is known that a linear two-weight code over a finite field $\F_q$ corresponds both to a multiset in a projective space over $\F_q$ that meets every hyperplane in either …
An Infinite Family of Quadratic Quadrinomial APN Functions
Carl Bracken, Eimear Byrne, Nadya Markin +1
We present an infinite family of quadratic APN functions on a finite field of dimension over GF(2) divisible by 3.
Linear-programming Decoding of Non-binary Linear Codes
Mark F. Flanagan, Vitaly Skachek, Eimear Byrne +1
We develop a framework for linear-programming (LP) decoding of non-binary linear codes over rings. We prove that the resulting LP decoder has the `maximum likelihood certificate' p…