  This paper examines finite field trigonometry as a tool to construct
trigonometric digital transforms. In particular, by using properties of the
k-cosine function over GF(p), the Finite Field Discrete Cosine Transform
(FFDCT) is introduced. The FFDCT pair in GF(p) is defined, having blocklengths
that are divisors of (p+1)/2. A special case is the Mersenne FFDCT, defined
when p is a Mersenne prime. In this instance blocklengths that are powers of
two are possible and radix-2 fast algorithms can be used to compute the
transform.
