- Communications Faculty of Sciences University Ankara Series A1 Mathematics and Statistics
- Vol: 68 Issue: 1
- k-autocorrelation and its applications
k-autocorrelation and its applications
Authors : Hayrullah Özimamoğlu, Murat Şahin, Oktay Ölmez
Pages : 672-685
Doi:10.31801/cfsuasmas.459971
View : 6 | Download : 6
Publication Date : 2019-02-01
Article Type : Research
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.Keywords : Autocorrelation, additive circulant codes, Fano plane