k-autocorrelation and its applications

Hayrullah Özimamoğlu; Murat Şahin; Oktay Ölmez

doi:10.31801/cfsuasmas.459971

Research Article

k-autocorrelation and its applications

Year 2019, Volume: 68 Issue: 1, 672 - 685, 01.02.2019

Hayrullah Özimamoğlu Murat Şahin , Oktay Ölmez

https://doi.org/10.31801/cfsuasmas.459971

https://izlik.org/JA57ZK26YX

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

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

Hayrullah Özimamoğlu Murat Şahin , Oktay Ölmez

https://doi.org/10.31801/cfsuasmas.459971

https://izlik.org/JA57ZK26YX

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	Research Article
Authors	Hayrullah Özimamoğlu This is me 0000-0001-7844-1840 Murat Şahin 0000-0002-9480-0433 Oktay Ölmez 0000-0002-9130-0038
Submission Date	December 12, 2017
Acceptance Date	March 27, 2018
Publication Date	February 1, 2019
DOI	https://doi.org/10.31801/cfsuasmas.459971
IZ	https://izlik.org/JA57ZK26YX
Published in Issue	Year 2019 Volume: 68 Issue: 1

Cite

APA	Özimamoğlu, H., Şahin, M., & Ölmez, O. (2019). k-autocorrelation and its applications. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 68(1), 672-685. https://doi.org/10.31801/cfsuasmas.459971
AMA	1.Özimamoğlu H, Şahin M, Ölmez O. k-autocorrelation and its applications. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68(1):672-685. doi:10.31801/cfsuasmas.459971
Chicago	Özimamoğlu, Hayrullah, Murat Şahin, and Oktay Ölmez. 2019. “K-Autocorrelation and Its Applications”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68 (1): 672-85. https://doi.org/10.31801/cfsuasmas.459971.
EndNote	Özimamoğlu H, Şahin M, Ölmez O (February 1, 2019) k-autocorrelation and its applications. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68 1 672–685.
IEEE	[1]H. Özimamoğlu, M. Şahin, and O. Ölmez, “k-autocorrelation and its applications”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 68, no. 1, pp. 672–685, Feb. 2019, doi: 10.31801/cfsuasmas.459971.
ISNAD	Özimamoğlu, Hayrullah - Şahin, Murat - Ölmez, Oktay. “K-Autocorrelation and Its Applications”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68/1 (February 1, 2019): 672-685. https://doi.org/10.31801/cfsuasmas.459971.
JAMA	1.Özimamoğlu H, Şahin M, Ölmez O. k-autocorrelation and its applications. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68:672–685.
MLA	Özimamoğlu, Hayrullah, et al. “K-Autocorrelation and Its Applications”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 68, no. 1, Feb. 2019, pp. 672-85, doi:10.31801/cfsuasmas.459971.
Vancouver	1.Özimamoğlu H, Şahin M, Ölmez O. k-autocorrelation and its applications. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. [Internet]. 2019 Feb. 1;68(1):672-85. Available from: https://izlik.org/JA57ZK26YX