Some Notes on the Generalized Cyclotomic Binary Sequences of Length 2pm and pm

Tongjiang YAN  Xiaoping LI  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E96-A    No.10    pp.2049-2051
Publication Date: 2013/10/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E96.A.2049
Print ISSN: 0916-8508
Type of Manuscript: LETTER
Category: Cryptography and Information Security
stream cipher,  linear complexity,  error linear complexity,  cyclotomic sequences,  tuple distribution,  

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This paper contributes to k-error linear complexity of some generalized cyclotomic binary sequences of length 2pm and pm constructed in recent years. By defining related reference sequences, we find that these sequences possess very low k-error linear complexity for some certain values of the parameter k even though they have high linear complexity. Moreover, we point out that (p-1)-tuple distributions of all these sequences are not span. Thus they should be selected carefully for use in stream cipher systems.