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In this paper, the k-trigonometric functions over the Galois Field GF(q) are introduced and their main properties derived. This leads to the definition of the cas k (.) function over GF(q), which in turn leads to a finite field Hartley Transform . The main properties of this new discrete transform are presented and areas for possible applications are mentioned.

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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.Comment: 5 pages, 1 table, Lecture Notes in Computer Science, LNCS 3124, Heidelberg: Springer Verlag, 2004, vol.1, pp.482-487, 200