Muhammad Imran

Exact quantum splitting and the structure of finite algebras

Berlekamp's algorithm factors a squarefree polynomial $f\in\mathbb{F}_q[x]$ by deterministic linear algebra, reducing the problem to splitting an explicit commutative algebra $B\cong\mathbb{F}_q^r$ into its $r$ simple factors. For large odd $q$, the standard efficient splitting step is randomized, while known derandomi...