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Optimal \((v,5,2,1)\) optical orthogonal codes of small \(v\)

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Abstract

We classify up to multiplier equivalence optimal \((v, 5, 2, 1)\) optical orthogonal codes (OOC) with \(v\le 114\). Examples of optimal \((v, 5, 2, 1)\) OOCs are presented for all \(v\le 155\), for which an optimal OOC exists.

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References

  1. Abdallah, W., Hamdi, M., Boudriga, N.: A public key algorithm for optical communication based on lattice cryptography. In: IEEE Symposium on Computers and Communications, vol. 5–8, pp. 200–205, July 2009

  2. Baicheva, T., Topalova, S.: Classification of optimal (v, 4, 1) binary cyclically permutable constant weight codes and cyclic S(2,4, v) designs with \(v\le 76\). Probl. Inf. Transm. 47(3), 224–231 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  3. Baicheva, T., Topalova, S.: Optimal (v,4,2,1) optical orthogonal codes with small parameters. J. Comb. Des. 20(2), 142–160 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  4. Bird, I.C.M., Keedwell, A.D.: Design and applications of optical orthogonal codes—a survey. Bull. Inst. Comb. Appl. 11, 21–44 (1994)

    MathSciNet  MATH  Google Scholar 

  5. Brand, N.: On the Bays–Lambossy theorem. Discret. Math. 78, 217–222 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  6. Buratti, M., Momihara, K., Pasotti, A.: New results on optimal \((v, 4, 2, 1)\) optical orthogonal codes. Des. Code Cryptogr. 58, 89–109 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  7. Buratti, M., Pasotti, A.: Further progress on difference families with block size 4 or 5. Des. Code Cryptogr. 56, 1–20 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  8. Buratti, M., Pasotti, A., Wu, D.: On optimal \((v,5,2,1)\) optical orthogonal codes. Des. Code Cryptogr. 68(1–3), 349–371 (2013)

  9. Chu, W., Colbourn, C.J.: Optimal (n, 4, 2)- OOC of small orders. Discret. Math. 279, 163–172 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  10. Chung, F.R.K., Salehi, J.A., Wei, V.K.: Optical orthogonal codes: design, analysis and applications. IEEE Trans. Inf. Theory 35, 595–604 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  11. Colbourn, C.J., Dinitz, J.H., Stinson, D.R.: Applications of combinatorial designs to communications, cryptography, and networking. In: Lamb, J.D., Preece, D.A. (eds.) Surveys in Combinatorics, pp. 37–100. Cambridge University Press, London (1999)

    Google Scholar 

  12. Fuji-hara, R., Miao, Y.: Optical orthogonal codes: their bounds and new optimal constructions. IEEE Trans. Inf. Theory 46, 2396–2406 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  13. Karp, R.M., Zhang, Y.: Randomized parallel algorithms for backtrack search and branch-and-bound computation. J. Assoc. Comput. Mach. (USA) 40(3), 765–789 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  14. Kaski, P., Östergård, P.: Classification Algorithms for Codes and Designs. Springer, Berlin (2006)

    MATH  Google Scholar 

  15. Mishima, M., Fu, H.L., Uruno, S.: Optimal conflict-avoiding codes of length \(n\equiv 0\) (mod 16) and weight 3. Des. Code Cryptogr. 52, 275–291 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  16. Momihara, K.: On cyclic \(2(k - 1)\)-support \((n, k)_{k-1}\) difference families. Finite Fields Appl. 15, 415–427 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  17. Momihara, K., Buratti, M.: Bounds and constructions of optimal (n, 4, 2, 1) optical orthogonal codes. IEEE Trans. Inf. Theory 55, 514–523 (2009)

    Article  MathSciNet  Google Scholar 

  18. Stinson, D.R., Wei, R., Yin, J.: Packings. In: Colbourn, C.J., Dinitz, J.H. (eds.) The CRC Handbook of Combinatorial Designs, 2nd edn, pp. 550–556. Chapman and Hall/CRC Press, Boca Raton, FL (2006)

    Google Scholar 

  19. Wang, X., Chang, Y.: Further results on \((v, 4, 1)\)-perfect difference families. Discret. Math. 310, 1995–2006 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  20. Wang, X., Chang, Y.: Further results on optimal \((v, 4, 2, 1)\)-OOCs. Discret. Math. 312, 331–340 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  21. Yang, G.C., Fuja, T.E.: Optical orthogonal codes with unequal auto- and cross-correlation constraints. IEEE Trans. Inf. Theory 41, 96–106 (1995)

    Article  MATH  Google Scholar 

  22. http://www.scc.acad.bg/articles/bluegene-quick-guide.pdf

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Acknowledgments

We are grateful to the Bulgarian National Supercomputing Centre for the permission to use its resources, and for the detailed instructions supplied by its team [22]. We would like to thank the anonymous referees for their adequate suggestions on the presentation of the material.

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Authors and Affiliations

  1. Institute of Mathematics and Informatics, P.O. Box 323, 5000, Veliko Tarnovo, Bulgaria

    Tsonka Baicheva & Svetlana Topalova

Authors
  1. Tsonka Baicheva
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  2. Svetlana Topalova
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Corresponding author

Correspondence to Tsonka Baicheva.

Additional information

This work was partially supported by the Bulgarian National Science Fund under Contract No. I01/0003.

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Baicheva, T., Topalova, S. Optimal \((v,5,2,1)\) optical orthogonal codes of small \(v\) . AAECC 24, 165–177 (2013). https://doi.org/10.1007/s00200-013-0192-1

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  • DOI: https://doi.org/10.1007/s00200-013-0192-1

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Mathematics Subject Classification (2000)