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math.NT2025
A general approach to permutation polynomials from quadratic forms
Ruikai Chen
We investigate a family of permutation polynomials of finite fields of characteristic 2. Through a connection between permutation polynomials and quadratic forms, a general treatme…
math.NT2025
On sesquilinear forms over finite fields
Ruikai Chen
We develop a theory of sesquilinear forms over finite fields, investigating their representations via polynomials and coefficient matrices, along with classification results for th…
math.NT2024
Classification of quadratic forms over finite fields with maximal and minimal Artin-Schreier curves
Ruikai Chen
This paper explores quadratic forms over finite fields with associated Artin-Schreier curves. Specifically, we investigate quadratic forms of represen…