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Linear complexity over F-q and over F-qm for linear recurring sequences

Meidl, Wilfried and Özbudak, Ferruh (2009) Linear complexity over F-q and over F-qm for linear recurring sequences. Finite Fields and Their Applications, 15 (1). pp. 110-124. ISSN 1071-5797

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Official URL: http://dx.doi.org/10.1016/j.ffa.2008.09.004

Abstract

Since the F-q-linear spaces F-q(m) and F-qm are isomorphic, an m-fold multisequence S over the finite field F-q with a given characteristic polynomial f is an element of F-q[x], can be identified with a single sequence S over F-qm with characteristic polynomial f. The linear complexity of S, which will be called the generalized joint linear complexity of S, can be significantly smaller than the conventional joint linear complexity of S. We determine the expected value and the variance of the generalized joint linear complexity of a random m-fold multisequence S with given minimal polynomial. The result on the expected value generalizes a previous result oil periodic m-fold multisequences. Moreover we determine the expected drop of linear complexity of a random m-fold multisequence with given characteristic polynomial f, when one switches from conventional joint linear complexity to generalized joint linear complexity.

Item Type:Article
Uncontrolled Keywords:Joint linear complexity; Generalized joint linear complexity; Multisequences; Linear recurring sequences
Subjects:UNSPECIFIED
ID Code:11480
Deposited By:Wilfried Meidl
Deposited On:29 Apr 2009 10:21
Last Modified:25 May 2011 14:07

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