Abstract:
The standard autocorrelation measures similarities between a binary sequence and its any shifted form. In this paper, we introduce the concept
of the k-autocorrelation of a binary sequence as a generalization of the standard autocorrelation. We give two applications of the k-autocorrelation. The
first one is related the additive circulant codes over F4 in coding theory. We
use the k-autocorrelation to determine the minimum distance of additive circulant codes over F4. The second one is related the (7; 3; 1)-BIBD in design
theory. The k-autocorrelation coefficients give us information about the lines
in the (7; 3; 1)-BIBD.