document: Linear complexity of polyphase power residue sequences The well known family of binary Legendre or quadratic residue sequences can be generalised to the multiple-valued case by employing a polyphase representation . These p-phase sequences , with p prime , also have prime length L , and can be constructed from the index sequence of length L or , equivalently , from the cosets of pth power residues and non-residues modulo-L . The linear complexity of these polyphase sequences is derived and shown to fall into four classes depending on the value assigned to b/sub 0 / , the initial digit of the sequence , and on whether p belongs to the set of pth power residues or not . The characteristic polynomials of the linear feedback shift registers that generate these sequences are also derived
doc_bio_tags: B I O B I I I O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O B I I I O O O O O O O