Skip to main content
SpringerLink
Log in

Two classes of optimal two-dimensional OOCs

  • Published:
Designs, Codes and Cryptography Aims and scope Submit manuscript

Abstract

Let Φ(u × v, k, λ a , λ c ) denote the largest possible size among all 2-D (u × v, k, λ a , λ c )-OOCs. In this paper, the exact value of Φ(u × v, k, λ a , k − 1) for λ a = k − 1 and k is determined. The case λ a = k − 1 is a generalization of a result in Yang (Inform Process Lett 40:85–87, 1991) which deals with one dimensional OOCs namely, u = 1.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Abel R.J.R., Buratti M.: Some progress on (v, 4, 1) difference families and optical orthogonal codes. J. Combin. Theory (A) 106, 59–75 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  2. Alderson T.L., Mellinger K.E.: Geometric constructions of optimal optical orthogonal codes. Adv. Math. Commun. 2, 451–467 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  3. Alderson T.L., Mellinger K.E.: Families of optimal OOCs with λ = 2. IEEE Trans. Inform. Theory 54, 3722–3724 (2008)

    Article  MathSciNet  Google Scholar 

  4. Alderson T.L., Mellinger K.E.: 2-Dimensional optical orthogonal codes from Singer groups. Discret. Appl. Math. 157, 3008–3019 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  5. Alem-Karladani M.M., Salehi J.A.: Spectral classification and multiplicative partitioning of constant-weight sequences based on circulant matrix representation of optical orthogonal codes. IEEE Trans. Inform. Theory 56, 4659–4667 (2010)

    Article  MathSciNet  Google Scholar 

  6. Buratti M.: Cyclic designs with block size 4 and related optimal optical orthogonal codes. Des. Codes Cryptogr. 26, 111–125 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  7. Cao H., Wei R.: Combinatorial constructions for optimal two-dimensional optical orthogonal codes. IEEE Trans. Inform. Theory 55, 1387–1394 (2009)

    Article  MathSciNet  Google Scholar 

  8. Chang Y., Ji L.: Optimal (4up, 5, 1) optical orthogonal codes. J Combin. Des. 12, 346–361 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  9. Chang Y., Miao Y.: Constructions for optimal optical orthogonal codes. Discret. Math. 261, 127–139 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  10. Chang Y., Yin J.: Further results on optimal optical orthogonal codes with weight 4. Discret. Math. 279, 135–151 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  11. Chang Y., Fuji-Hara R., Miao Y.: Combinatorial constructions of optimal optical orthogonal codes with weight 4. IEEE Trans. Inform. Theory 49, 1283–1292 (2003)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  13. Chu W., Colbourn C.J.: Recursive constructions for optimal (n, 4, 2)-OOCs. J. Combin. Des. 12, 333–345 (2004)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  15. Feng T., Chang Y., Ji L.: Constructions for strictly cyclic 3-designs and applications to optimal OOCs with λ = 2. J. Combin. Theory (A) 115, 1527–1551 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  16. Fuji-Hara R., Miao Y.: Optimal orthogonal codes: their bounds and new optimal constructions. IEEE Trans. Inform. Theory 46, 2396–2406 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  17. Ge G., Yin J.: Constructions for optimal (v, 4, 1) optical orthogonal codes. IEEE Trans. Inform. Theory 47, 2998–3004 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  18. Kwong W.C., Perrier P.A., Prucnal P.R.: Performance comparison of asynchronous and synchronous code-division multiple-access techniques for fiber-optic local area networks. IEEE Trans. Commun. 39, 1625–1634 (1991)

    Article  Google Scholar 

  19. Ma S., Chang Y.: A new class of optimal optical orthogonal codes with weight five. IEEE Trans. Inform. Theory 50, 1848–1850 (2004)

    Article  MathSciNet  Google Scholar 

  20. Ma S., Chang Y.: Constructions of optimal optical orthogonal codes with weight five. J. Combin. Des. 13, 54–69 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  21. Maric S.V., Lau V.K.N.: Multirate fiber-optic CDMA: system design and performance analysis. J. Lightwave Technol. 16, 9–17 (1998)

    Article  Google Scholar 

  22. Maric S.V., Moreno O., Corrada C.: Multimedia transmission in fiber-optic LANs using optical CDMA. J. Lightwave Technol. 14, 2149–2153 (1996)

    Article  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  24. Omrani R., Garg G., Kumar P.V., Elia P., Bhambhani P.: Large families of optimal two-dimensional optical orthogonal codes. E-print: arXiv:0911.0143, 11 (2009).

  25. Salehi J.A.: Code division multiple-access techniques in optical fiber networks-Part I: fundamental principles. IEEE Trans. Commun. 37, 824–833 (1989)

    Article  Google Scholar 

  26. Salehi J.A., Brackett C.A.: Code division multiple-access techniques in optical fiber networks-Part II: systems performance analysis. IEEE Trans. Commun. 37, 834–842 (1989)

    Article  Google Scholar 

  27. Shivaleela E.S., Selvarajan A., Srinivas T.: Two-dimensional optical orthogonal codes for fiber-optic CDMA networks. J. Lightwave Technol. 23, 647–654 (2005)

    Article  Google Scholar 

  28. Stinson D.R.: Combinatorial Designs: Constructions and Analysis. Springer, New York (2004)

    MATH  Google Scholar 

  29. Sun S., Yin H., Wang Z., Xu A.: A new family of 2-D optical orthogonal codes and analysis of its performance in optical CDMA access networks. J. Lightwave Technol. 24, 1646–1653 (2006)

    Article  Google Scholar 

  30. van Lint J.H., Wilson R.M.: A Course in Combinatorics, 2nd edn. Cambridge University Press, Cambridge (2001)

    MATH  Google Scholar 

  31. Wang X., Chang Y.: Further results on optimal (v, 4, 2, 1)-OOCs, submitted.

  32. Wang J., Shan X., Yin J.: On constructions for optimal two-dimentional optical orthogonal codes. Des. Codes Cryptogr. 54, 43–60 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  33. Yang Y.: New enumeration results about the optical orthogonal codes. Inform. Process. Lett. 40, 85–87 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  34. Yang G.C., Kwong W.C.: Performance comparison of multiwavelength CDMA and WDMA+CDMA for fiber-optic networks. IEEE Trans. Commun. 45, 1426–1434 (1997)

    Article  Google Scholar 

  35. Yin J.: Some combinatorial constructions for optical orthogonal codes. Discret. Math. 185, 201–219 (1998)

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Mathematics, Beijing Jiaotong University, Beijing, 100044, People’s Republic of China

    Yuemei Huang & Yanxun Chang

Authors
  1. Yuemei Huang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yanxun Chang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yanxun Chang.

Additional information

Communicated by J. Jedwab.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Huang, Y., Chang, Y. Two classes of optimal two-dimensional OOCs. Des. Codes Cryptogr. 63, 357–363 (2012). https://doi.org/10.1007/s10623-011-9560-7

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10623-011-9560-7

Keywords

Mathematics Subject Classification (2000)

Search

Navigation