Implementing Basic Arithmetic in ${\mathbb{F}}_p$ via ${\mathbb{F}}_2$, and Its Application for Computing the Hamming Distance of Linear Codes

Fernando Hernando, Gregorio Quintana-Ortí

We present a new general method for performing basic arithmetic in the finite field~${\mathbb{F}}_p$ for any prime $p>2$ by using traditional binary operations over~${\mathbb{F}}_2$. O…