Actions of the Unitary Group on Irreducible/Primitive Polynomials and Their Applications to Randomness of Sequences

This paper investigates how irreducibility and primitivity can be preserved when the unitary group acts on irreducible or primitive polynomials. Applying these operators to sequences and their discrete Fourier spectra, the weight preserving property is obtained. Some new randomness criteria are introduced in terms of these operators, which are suitable for measuring unpredictibility of pseudo-random sequences employed in stream ciphers.