Longjiang Qu

New Permutation Trinomials Constructed from Fractional Polynomials

2016 · arXiv (Cornell University)

Permutation trinomials over finite fields consititute an active research due to their simple algebraic form, additional extraordinary properties and their wide applications in many areas of science and engineering. In the present paper, six new …

The Endomorphism Rings of Supersingular Elliptic Curves over $\mathbb{F}_p$ and the Binary Quadratic Forms

2022 · arXiv (Cornell University)

It is well known that there is a one-to-one correspondence between supersingular $j$-invariants up to the action of $\text{Gal}(\mathbb{F}_{p^2}/\mathbb{F}_p)$ and type classes of maximal orders in $B_{p,\infty}$ by Deuring's theorem. Interestingly, we establish a one-to-one …