k-autocorrelation and its applications

Authors : Hayrullah ÖZİMAMOĞLU, Murat ŞAHİN, Oktay ÖLMEZ

Pages : 672-685

Doi:10.31801/cfsuasmas.459971

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Publication Date : 2019-02-01

Article Type : Research Paper

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 insert ignore into journalissuearticles values(7,3,1);-BIBD in design theory. The k-autocorrelation coefficients give us information about the lines in the insert ignore into journalissuearticles values(7,3,1);-BIBD.
Keywords : Autocorrelation, additive circulant codes, Fano plane