Title: On the k-error linear complexity of generalised cyclotomic sequences

Authors: Longfei Liu; Xiaoyuan Yang; Xiaoni Du; Bin Wei

Addresses: Key Laboratory of Network and Information Security of APF, Engineering College of APF, Xi'an 710086, China ' Key Laboratory of Network and Information Security of APF, Engineering College of APF, Xi'an 710086, China; Key Laboratory of Computer Network and Information Security of the Ministry of Education, Xidian University, Xi'an 710071, China ' Key Laboratory of Computer Network and Information Security of the Ministry of Education, Xidian University, Xi'an 710071, China ' Key Laboratory of Network and Information Security of APF, Engineering College of APF, Xi'an 710086, China

Abstract: Generalised cyclotomic binary sequences are divided into Whiteman-generalised cyclotomic and Ding-generalised cyclotomic. Firstly, two classes of error generalised cyclotomic sequences with length pq over Z_pq are constructed; secondly, k-error linear complexity of generalised cyclotomic sequences are considered, using the trace representation and cyclotomic theory, respectively. It is shown that k-error linear complexity of generalised cyclotomic sequences do not exceed p + q-1 which is much less than the (zero-error) linear complexity.

Keywords: stream cipher; pseudo-random sequences; generalised cyclotomy; k-error linear complexity; trace representation; cyclotomic theory.

DOI: 10.1504/IJHPCN.2016.080411

International Journal of High Performance Computing and Networking, 2016 Vol.9 No.5/6, pp.394 - 400

Received: 25 Jul 2014
Accepted: 15 Oct 2014
Published online: 22 Nov 2016 *

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