A new generic generating algorithm for rank n integer DCT transform radix

In this paper, a new generic generating algorithm for rank n integer DCT transform radix is proposed. The relation of amounts of coefficients in radix and rank of matrix and an generic generating algorithm for rank n (n=2
^k
,k>0) integer DCT transform radix are found and proved in this paper based on theory of integer DCT and characteristic of cosine function. Through reordering variations of coefficient, the mid-polynomials have strong laws. The group of polynomials in N variable is resolved by design a N-digits with M as radix implementing N-loops. The experimental result show that the algorithm can find all valid radix for n×n (n=2
^k
,k>0) integer DCT if computers power enough.