2-dimensional optical orthogonal codes from Singer groups. (English) Zbl 1196.94090
Using the construction (of OOCs) in a previous paper [Adv. Math. Commun. 2, No. 4, 451–467 (2008; Zbl 1155.94021)] new families of 2-dimensional OOCs codes are presented. With respect to the Johnson bound (related to the maximal number of codewords) the codes constructed are either optimal or are asymptotically optimal. The constructed codes have more flexible dimensions and weight than the previously known J-optimal families.
Reviewer: Piroska Lakatos (Debrecen)
MSC:
| 94B27 | Geometric methods (including applications of algebraic geometry) applied to coding theory |
| 94B60 | Other types of codes |
| 05B25 | Combinatorial aspects of finite geometries |
| 94A29 | Source coding |
Citations:
Zbl 1155.94021References:
| [1] | Alderson, T. L.; Mellinger, K. E., Families of optimal oocs with \(\lambda = 2\), IEEE Trans. Inform. Theory, 54, 8, 3722-3724 (2008) · Zbl 1305.94113 |
| [2] | Alderson, T. L.; Mellinger, K. E., Geometric constructions of optimal optical orthogonal codes, Adv. Math. Commun., 2, 4, 451-467 (2008) · Zbl 1155.94021 |
| [3] | Chung, F. R.K.; Salehi, J. A.; Wei, V. K., Optical orthogonal codes: Design, analysis, and applications, IEEE Trans. Inform. Theory, 35, 3, 595-604 (1989) · Zbl 0676.94021 |
| [4] | Chung, H.; Kumar, P. V., Optical orthogonal codes — new bounds and an optimal construction, IEEE Trans. Inform. Theory, 36, 4, 866-873 (1990) · Zbl 0707.94024 |
| [5] | Drudge, K., On the orbits of Singer groups and their subgroups, Electron. J. Combin., 9, 1, 10 pp. (2002), Research Paper 15 (electronic) · Zbl 0998.20003 |
| [6] | Hirschfeld, J. W.P., Projective geometries over finite fields, (Oxford Mathematical Monographs (1998), The Clarendon Press Oxford University Press: The Clarendon Press Oxford University Press New York) · Zbl 0899.51002 |
| [7] | Lee, S.-S.; Seo, S.-W., New construction of multiwavelength optical orthogonal codes, IEEE Trans. Commun., 50, 12, 2003-2008 (2002) |
| [8] | Morelle, M.; Goursaud, C.; Julien-Vergonjanne, A.; Aupetit-Berthelemot, C.; Cances, J.-P.; Dumas, J.-M.; Guignard, P., 2-dimensional optical cdma system performance with parallel interference cancellation, Microprocess. Microsyst., 31, 4, 215-221 (2007) |
| [9] | Omrani, R.; Elia, P.; Kumar, P. V., New constructions and bounds for 2-d optical orthogonal codes, (Helleseth, T.; Sarwate, D. V.; Song, H.-Y.; Yang, K., SETA. SETA, Lecture Notes in Computer Science, vol. 3486 (2004), Springer) · Zbl 1145.94478 |
| [10] | Omrani, R.; Kumar, P. V., Codes for optical CDMA, (SETA. SETA, Lecture Notes in Computer Science, vol. 4086 (2006), Springer) · Zbl 1152.94371 |
| [11] | R. Omrani, O. Moreno, P. Kumar, Improved Johnson bounds for optical orthogonal codes with \(\lambda > 1\); R. Omrani, O. Moreno, P. Kumar, Improved Johnson bounds for optical orthogonal codes with \(\lambda > 1\) |
| [12] | R. Omrani, O. Moreno, P. Kumar, A generalized Bose-Chowla family of optical orthogonal codes and distinct difference sets, IEEE Trans. Inform. Theory 53 (5); R. Omrani, O. Moreno, P. Kumar, A generalized Bose-Chowla family of optical orthogonal codes and distinct difference sets, IEEE Trans. Inform. Theory 53 (5) · Zbl 1316.94120 |
| [13] | Xu, C.; Yang, Y. X., Algebraic constructions of asymptotically optimal two-dimensional optical orthogonal codes, Chinese. Sci. Bull., 42, 19, 1659-1662 (1997) · Zbl 0923.94043 |
| [14] | Yang, G.-C.; Kwong, W., Two-dimensional spatial signature patterns, IEEE Trans. Commun., 44, 2, 184-191 (1996) |
| [15] | Yang, G.-C.; Kwong, W., Performance comparison of multiwavelength cdma and wdma + cdma for fiber-optic networks, IEEE Trans. Commun., 45, 11, 1426-1434 (1997) |
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