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Dergiler / Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics / 2026 / Volume: 68 Issue: 1

k-autocorrelation and its applications

Hayrullah Özimamoğlu0000-0001-7844-1840
Murat Şahin0000-0002-9480-0433
Oktay Ölmez0000-0002-9130-0038
Sayfa
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Yayın Tarihi
2019-02-01
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

The k-autocorrelation coefficients give us information about the lines in the (7,3,1)-BIBD.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:The standard autocorrelation measures similarities between a binary sequence and its any shifted form.
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Temel Bulgular & Veri:The second one is related the (7,3,1)-BIBD in design theory.
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Sonuç & Katkı:The k-autocorrelation coefficients give us information about the lines in the (7,3,1)-BIBD.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler: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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Bu Makaleye Atıf Yap

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

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Kaynakça (6)

  1. Danielsen, L.E. and Parker, M.G., Directed Graph Representation of Half-Rate Additive Codes over GF(4), Des. Codes Cryptogr., 59 (2011), 119-130.
  2. Hertel, D., Crosscorrelation Properties between Perfect Sequences, Sequences and Their Applications-SETA, 2004.
  3. Huffman, W.C. and Pless, V., Fundamentals of Error Correcting Codes, Cambridge University Press, 2003.
  4. Ling, S. and Xing, C., Coding Theory, U.K.:, Cambridge Univ. Press, 2004.
  5. Stinson, D.R., Combinatorial Designs:, Construction and Analysis, Springer, 2003.
  6. White, G. and Grassl, M., A New Minimum Weight Algorithm for Additive Codes, International Symposium on Information Theory; (2006), 1119-1123.