A coefficient test for fourth degree permutation polynomials over integer rings

So far, there are known conditions on a polynomial's coefficients so that it is a permutation polynomial (PP) modulo a given positive integer number only for degrees up to three. For polynomials of degrees higher than three, we only know the conditions so that they are PPs modulo a power of two. In this paper, we propose a coefficient test for fourth degree polynomials to be PPs over integer rings. The test is useful for finding fourth degree PPs for different applications in communications such as interleavers for turbo codes.