构造一系列新的最优循环填充及其相应的光正交码
Constructions of a New Infinite Class of Optimal Cyclic Packing and Their Related OOCs
摘要: 循环填充是构造光正交码的有效方法之一。对于任何素数p≡3(mod4)且p≥7，本文通过构造一系列新的区组大小为3和7的循环填充从而得到相应的新的码长为27p码重是w={3,7}的最优变重量光正交码。
Abstract: Cyclic packing is one of efficient approaches for constructing optical orthogonal code (OOC). In this paper, a new infinite class of optimal variable-weight with length 27p and weights w={3,7} are obtained via constructing cyclic packing with blocks 3 and 7, for any prime p≡3(mod4) and p≥7.
文章引用：黄必昌. 构造一系列新的最优循环填充及其相应的光正交码[J]. 理论数学, 2019, 9(9): 1036-1042. https://doi.org/10.12677/PM.2019.99129

参考文献

[1] Salehi, J.A. (1989) Code Division Multiple-Access Techniques in Optical Fiber Networks Part I: Fundamental Principles. IEEE Transactions on Communications, 37, 824-833. [Google Scholar] [CrossRef] 
[2] Yang, G.C. (1996) Variable-Weight Optical Orthogonal Codes for CDMA Network with Multiple Performance Requirements. IEEE Transactions on Communications, 44, 47-55. [Google Scholar] [CrossRef] 
[3] Yang, G.C. and Kwong, W.C. (2002) Prime Codes with Applications to CDMA Optical and Wireless Networks. Artech House, Nor-wood.
[4] Yin, J. (1998) Some Combinatorial Constructions for Optical Orthogonal Codes. Discrete Mathematics, 185, 201-219. [Google Scholar] [CrossRef] 
[5] Wu, D.H., Zhao, H.M., Fan, P.Z., et al. (2010) Optimal Variable-Weight Optical Orthogonal Codes via Difference Packings. IEEE Transactions on Information Theory, 56, 4053-4060. [Google Scholar] [CrossRef] 
[6] Chang, Y., Fuji-Hara, R. and Miao, Y. (2003) Combinatorial Constructions of Optimal Optical Orthogonal Codes with Weight 4. IEEE Transactions on Information Theory, 49, 1283-1292. [Google Scholar] [CrossRef] 
[7] Chang, Y. and Miao, Y. (2003) Constructions for Optimal Optical Orthogonal Codes. Discrete Mathematics, 261, 127-139. [Google Scholar] [CrossRef] 
[8] Fuji-Hara, R., Miao, Y. and Yin, J. (2001) Optimal Optical Orthogonal Codes. SIAM Journal on Discrete Mathematics, 14, 256-266. [Google Scholar] [CrossRef] 
[9] Ge, G. and Yin, J. (2001) Constructions for Optimal Optical Orthogonal Codes. IEEE Transactions on Information Theory, 47, 2998-3004. [Google Scholar] [CrossRef] 
[10] Ma, S. and Chang, Y. (2005) Constructions of Optimal Optical Orthogonal Codes with Weight Five. Journal of Combinatorial Designs, 13, 54-69. [Google Scholar] [CrossRef] 
[11] Chang, Y. and Ji, L. (2004) Optimal Optical Orthogonal Codes. Journal of Combinatorial Designs, 12, 346-361. [Google Scholar] [CrossRef] 
[12] Chen, K., Wei, R. and Zhu, L. (2012) Existence of Difference Families with q a Prime Power. Journal of Combinatorial Designs, 10, 126-138. [Google Scholar] [CrossRef] 
[13] Jiang, J., Wu, D.H. and Fan, P.Z. (2011) Senior Member, IEEE, General Constructions of Optimal Variable-Weight Optical Orthogonal Codes. IEEE Transactions on Information Theory, 57, 4488-4496. [Google Scholar] [CrossRef] 
[14] Wu, D., Chen, Z. and Cheng, M. (2008) A Note on the Existence of Balanced Difference Families. The Australasian Journal of Combinatorics, 41, 171-174.
[15] Zhao, H.M., Wu, D.H. and Fan, P.Z. (2010) Constructions of Optimal Variable-Weight Optical Orthogonal Codes. Journal of Combinatorial Designs, 18, 274-291. [Google Scholar] [CrossRef] 
[16] Buratti, M., Wei, Y.E., Wu, D.H., Fan, P.Z. and Cheng, M.Q. (2011) Relative Difference Families with Variable Block Sizes and Their Related OOCs. IEEE Transactions on Information Theory, 47, 7489-7497. [Google Scholar] [CrossRef] 
[17] Liu, Y. and Wu, D.H. (2013) Constructions of Optimal Variable-Weight OOCs via Quadratic Residues. Frontiers of Mathematics in China, 8, 869-890. [Google Scholar] [CrossRef] 
[18] Zhong, X.R., Wu, D.H. and Fan, P.Z. (2012) New Infinite Classes of Optimal Optical Orthogonal Codes via Quadratic Residues. IEICE Transactions, 95, 1827-1834. [Google Scholar] [CrossRef] 
[19] Nathanson, M.B. (2000) Elementary Methods in Number The-ory. Springer-Verlag, New York.

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