Research Article
Year 2019,
Volume: 68 Issue: 1, 672 - 685, 01.02.2019
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.
References
- 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.
- Hertel, D., Crosscorrelation Properties between Perfect Sequences, Sequences and Their Applications-SETA, 2004.
- Huffman, W.C. and Pless, V., Fundamentals of Error Correcting Codes, Cambridge University Press, 2003.
- Ling, S. and Xing, C., Coding Theory, U.K.:, Cambridge Univ. Press, 2004.
- Stinson, D.R., Combinatorial Designs:, Construction and Analysis, Springer, 2003.
- White, G. and Grassl, M., A New Minimum Weight Algorithm for Additive Codes, International Symposium on Information Theory; (2006), 1119-1123.
Year 2019,
Volume: 68 Issue: 1, 672 - 685, 01.02.2019
Abstract
References
- 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.
- Hertel, D., Crosscorrelation Properties between Perfect Sequences, Sequences and Their Applications-SETA, 2004.
- Huffman, W.C. and Pless, V., Fundamentals of Error Correcting Codes, Cambridge University Press, 2003.
- Ling, S. and Xing, C., Coding Theory, U.K.:, Cambridge Univ. Press, 2004.
- Stinson, D.R., Combinatorial Designs:, Construction and Analysis, Springer, 2003.
- White, G. and Grassl, M., A New Minimum Weight Algorithm for Additive Codes, International Symposium on Information Theory; (2006), 1119-1123.
There are 6 citations in total.
Details
| Primary Language | English |
|---|---|
| Journal Section | Review Articles |
| Authors | |
| Publication Date | February 1, 2019 |
| Submission Date | December 12, 2017 |
| Acceptance Date | March 27, 2018 |
| Published in Issue | Year 2019 Volume: 68 Issue: 1 |
Cite
Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.
