On Reed-Muller subcodes, Grassmannian partitions and sum-free functions

Philipp Heering, Christian Kaspers, Vladislav Taranchuk

A function $F:{\mathbb{F}}_2^n\to {\mathbb{F}}_2^m$ is called $k$th-order sum-free if the sum of its values over any $k$-dimensional affine subspace of ${\mathbb{F}}_2^n$ is non-…