On the structure of Sidel´nikov sequences for Pythagorean primes

Pseudo-noise (PN) sequences (also known as a spreading code) are commonly employed in spread-spectrum (SS) multi-access systems via techniques like frequency-hopping (FHSS) or direct-sequence (DSSS). In this paper we exploit the algebraic structure of a class of PN sequences (that of M-ary Sidel´nikov sequences) in order to efficiently derive its complete set in time and frequency domains. Our group theoretic approach only requires an initial sequence, its discrete Fourier transform and a small number of distinct permutations thus making it a fast generation method viable for many wireless or tethered communication systems.