Formula omitted]-Kerdock codes and pseudorandom binary sequences

Abstract

The Z 8 -analogues of the Kerdock codes of length n=2 m 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 m 4. 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 Z 2 l ,l⩾4 is sketched out.