Arithmetic of finite fields

The arithmetic operations in finite fields and their implementation are important to the construction of error detecting and correcting codes. The addition, multiplication and division in the field GF(2^m) are implemented as polynomial operations using binary logic of flip-flops and EXOR´s. For fields of non-binary characteristic, modular arithmetic (with modulus p, a prime) becomes important. This paper focuses on problems relating to the arithmetic of GF(p), and some recent results and new ideas on this topic are presented here.