Z8-Kerdock codes and pseudorandom binary sequences

Abstract

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 n. 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. © 2003 Published by Elsevier Inc.