Multi-Rate Representation of Generalized Cyclotomic Sequences of Any Odd Period

Chuan LV  Tongjiang YAN  Guozhen XIAO  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E98-A   No.11   pp.2301-2306
Publication Date: 2015/11/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E98.A.2301
Type of Manuscript: PAPER
Category: Cryptography and Information Security
generalized cyclotomic sequence,  d-residue sequence,  linear complexity,  

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Based on a unified representation of generalized cyclotomic classes, every generalized cyclotomic sequence of order d over $Z_{p_{1}^{e_{1}}p_{2}^{e_{2}}cdots p_{r}^{e_{r}}}$ is shown to be a sum of d-residue sequences over $Z_{p_{s}^{e_{s}}}$ for $sin {1,2,cdots,r }$. For d=2, by the multi-rate approach, several generalized cyclotomic sequences are explicitly expressed by Legendre sequences, and their linear complexity properties are analyzed.