Splitting sums of binary polynomials
Abstract
We study an analogue of a classical arithmetic problem over the ring of polynomials. We prove that $m = 5$ is the minimal number such that the sums of any two distinct polynomials in a set of $m$ polynomials over $\F_2[x]$ cannot all be of the form $x^k(x+1)^{\ell}$.
Fields of Study & Subjects
Coding theory and cryptography
Advanced Combinatorial Mathematics
Limits and Structures in Graph Theory
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 13 February 2026
- Language
- EN
- Document type
- Preprint