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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
The k-autocorrelation coefficients give us information about the lines in the (7,3,1)-BIBD.
📌 3 Key Takeaways
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Objective & Hypothesis:The standard autocorrelation measures similarities between a binary sequence and its any shifted form.
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Key Findings & Data:The second one is related the (7,3,1)-BIBD in design theory.
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Conclusion & Impact:The k-autocorrelation coefficients give us information about the lines in the (7,3,1)-BIBD.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Autocorrelation · additive circulant codes · Fano plane
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.
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Cite This Article
Özimamoğlu, H., Şahin, M., Ölmez, O. (2019). k-autocorrelation and its applications. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, Volume: 68 Issue: 1. https://doi.org/10.31801/cfsuasmas.459971