k-autocorrelation and its applications

Hayrullah Özimamoğlu; Murat Şahin; Oktay Ölmez

doi:10.31801/cfsuasmas.459971

Araştırma Makalesi

k-autocorrelation and its applications

Yıl 2019, Cilt: 68 Sayı: 1, 672 - 685, 01.02.2019

Hayrullah Özimamoğlu Murat Şahin , Oktay Ölmez

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

Öz

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.

Anahtar Kelimeler

Autocorrelation, additive circulant codes, Fano plane

Kaynakça

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.

Yıl 2019, Cilt: 68 Sayı: 1, 672 - 685, 01.02.2019

Hayrullah Özimamoğlu Murat Şahin , Oktay Ölmez

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

Öz

Kaynakça

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.

Toplam 6 adet kaynakça vardır.

Ayrıntılar

Birincil Dil	İngilizce
Bölüm	Makaleler
Yazarlar	Hayrullah Özimamoğlu 0000-0001-7844-1840 Murat Şahin 0000-0002-9480-0433 Oktay Ölmez 0000-0002-9130-0038
Yayımlanma Tarihi	1 Şubat 2019
Gönderilme Tarihi	12 Aralık 2017
Kabul Tarihi	27 Mart 2018
Yayımlandığı Sayı	Yıl 2019 Cilt: 68 Sayı: 1

Kaynak Göster

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	Özimamoğlu H, Şahin M, Ölmez O. k-autocorrelation and its applications. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. Şubat 2019;68(1):672-685. doi:10.31801/cfsuasmas.459971
Chicago	Özimamoğlu, Hayrullah, Murat Şahin, ve Oktay Ölmez. “K-Autocorrelation and Its Applications”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68, sy. 1 (Şubat 2019): 672-85. https://doi.org/10.31801/cfsuasmas.459971.
EndNote	Özimamoğlu H, Şahin M, Ölmez O (01 Şubat 2019) k-autocorrelation and its applications. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68 1 672–685.
IEEE	H. Özimamoğlu, M. Şahin, ve O. Ölmez, “k-autocorrelation and its applications”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., c. 68, sy. 1, ss. 672–685, 2019, doi: 10.31801/cfsuasmas.459971.
ISNAD	Özimamoğlu, Hayrullah vd. “K-Autocorrelation and Its Applications”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68/1 (Şubat 2019), 672-685. https://doi.org/10.31801/cfsuasmas.459971.
JAMA	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 vd. “K-Autocorrelation and Its Applications”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, c. 68, sy. 1, 2019, ss. 672-85, doi:10.31801/cfsuasmas.459971.
Vancouver	Özimamoğlu H, Şahin M, Ölmez O. k-autocorrelation and its applications. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68(1):672-85.