Journals / Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics / 2019 / Cilt: 68 - Sayı: 1
k-AUTOCORRELATION AND ITS APPLICATIONS
- Journal
- Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics
- Pages
- 672–685
- DOI
- —
Abstract
The standard autocorrelation measures similarities between a binary sequence and its any shifted form. In this paper, we introduce the conceptof the k-autocorrelation of a binary sequence as a generalization of the standard autocorrelation. We give two applications of the k-autocorrelation. TheÖrst one is related the additive circulant codes over F4 in coding theory. Weuse 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 designtheory. The k-autocorrelation coe¢ cients give us information about the linesin the (7; 3; 1)-BIBD.