On Maximal Families of Binary Polynomials with Pairwise Linear Common Factors

arXiv:2405.08741v1 Announce Type: cross
Abstract: We consider the construction of maximal families of polynomials over the finite field $\mathbb{F}_q$, all having the same degree $n$ and a nonzero constant term, where the degree of the GCD of any two polynomials is $d$ with $1 \le d\le n$. The motivation for this problem lies in a recent construction for subspace codes based on cellular automata. More precisely, the minimum distance of such subspace codes relates to the maximum degree $d$ of …

arxiv binary construction cs.cr cs.dm families linear math.co motivation