Paper 2004/228

DISTRIBUTION OF R-PATTERNS IN THE KERDOCK-CODE BINARY SEQUENCES AND THE HIGHEST LEVEL SEQUENCES OF PRIMITIVE SEQUENCES OVER $Z_{2^l}$

Honggang Hu and Dengguo Feng

Abstract

The distribution of r-patterns is an important aspect of pseudorandomness for periodic sequences over finite field.The aim of this work is to study the distribution of r-patterns in the Kerdock-code binary sequences and the highest level sequences of primitive sequences over $Z_{2^l}$.By combining the local Weil bound with spectral analysis,we derive the upper bound of the deviation to uniform distribution.As a consequence,the recent result on the quantity is improved.