Designs, Codes and Cryptography

, Volume 42, Issue 2, pp 181–193

Remarks on the k-error linear complexity of pn-periodic sequences


DOI: 10.1007/s10623-006-9029-2

Cite this article as:
Meidl, W. & Venkateswarlu, A. Des Codes Crypt (2007) 42: 181. doi:10.1007/s10623-006-9029-2


Recently the first author presented exact formulas for the number of 2n-periodic binary sequences with given 1-error linear complexity, and an exact formula for the expected 1-error linear complexity and upper and lower bounds for the expected k-error linear complexity, k ≥ 2, of a random 2n-periodic binary sequence. A crucial role for the analysis played the Chan–Games algorithm. We use a more sophisticated generalization of the Chan–Games algorithm by Ding et al. to obtain exact formulas for the counting function and the expected value for the 1-error linear complexity for pn-periodic sequences over \({\mathbb{F}_{p, p}}\) prime. Additionally we discuss the calculation of lower and upper bounds on the k-error linear complexity of pn-periodic sequences over \({\mathbb{F}_{p}}\) .


Linear complexity k-error linear complexity Chan-Games algorithm Periodic sequences Stream cipher 

AMS Classifications

94A55 94A60 11B50 

Copyright information

© Springer Science+Business Media, LLC 2006

Authors and Affiliations

  1. 1.Sabanci UniversityIstanbulTurkey
  2. 2.Temasek LaboratoriesNational University of SingaporeSingaporeSingapore

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