Z8-Kerdock codes and pseudorandom binary sequences

Z8-Kerdock codes and pseudorandom binary sequences

The Z8 -analogues of the Kerdock codes of length n=2m were introduced by Carlet in 1998. We study the binary sequences of period n - 1 obtained from their cyclic version by using the most significant bit (MSB)-map.The relevant Boolean functions are of degree 4 in general. The linear span of t...

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Bibliographic Details
Main Authors: Lahtonen, Jyrki, Ling, San, Sole, Patrick, Zinoviev, Dmitrii
Other Authors: School of Physical and Mathematical Sciences
Format: Article
Language:English
Published: 2013
Subjects:
DRNTU::Engineering::Computer science and engineering::Data::Coding and information theory
Online Access:https://hdl.handle.net/10356/98360
http://hdl.handle.net/10220/9844
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Institution: Nanyang Technological University
Language: English
Description
Summary:The Z8 -analogues of the Kerdock codes of length n=2m were introduced by Carlet in 1998. We study the binary sequences of period n - 1 obtained from their cyclic version by using the most significant bit (MSB)-map.The relevant Boolean functions are of degree 4 in general. The linear span of these sequences has been known to be of the order of m4. We will show that the crosscorrelation and nontrivial autocorrelation of this family are both upper bounded by a small multiple of v4. The nonlinearity of these sequences has a similar lower bound. A generalization of the above results to the alphabet Z2l, l >= 4 is sketched out.

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