The relationship between amounts of coefficients and order in radix is discovered through research of DCT principle and proven in combination with the nature of cosine function. On this basis

a generic generating algorithm for N-order (N=2

k>0

sic passim) integer DCT transform radix is presented

which we do not need to analyze floating radix corresponding to integer’s. Through rearrange variations of coefficient

the mid-polynomials are extremely regularity. The group of polynomials in arbitrary N-variable is resolved by designing a N-digits with M as radix implementing N-loops to exhaust all possible solutions. The experimental results show that the algorithm can find all available radix for arbitrary N×N integer DCT as long as the computing capacity is enough.