Z8-Kerdock codes and pseudorandom binary sequences
Date of Issue2003
School of Physical and Mathematical Sciences
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.
DRNTU::Engineering::Computer science and engineering::Data::Coding and information theory
Journal of complexity
© 2003 Elsevier Inc. This is the author created version of a work that has been peer reviewed and accepted for publication by Journal of Complexity, Elsevier Inc. It incorporates referee’s comments but changes resulting from the publishing process, such as copyediting, structural formatting, may not be reflected in this document. The published version is available at: [http://dx.doi.org/10.1016/j.jco.2003.08.014].