Block (cyclic) channel coding standards for third generation cellular networks require the implementation of high-performance burst-error detection and correction algorithms. Galois field (GF) arithmetic is commonly used in these architecture for encoding and decoding error codes, however, many architectures still do not support dedicated functional units. This paper presents the design of a generic parallel finite-field GF(2m) multiplier targeted at DSP and embedded processors. As opposed to previous research, this design has the ability to utilize different primitive polynomials as an input, thereby, being able to be reprogrammable. Moreover, a design is presented that is a combined binary and finite-field GF(2m) multiplier. Area, delay, and power dissipation results are presented from several ASIC libraries.