Frontiers of Mathematics in China >
Constructions of optimal variable-weight OOCs via quadratic residues
Received date: 26 Jul 2011
Accepted date: 13 May 2012
Published date: 01 Aug 2013
Copyright
Variable-weight optical orthogonal code (OOC) was introduced by G. C. Yang [IEEE Trans. Commun., 1996, 44: 47-55] for multimedia optical CDMA systems with multiple quality of service (QoS) requirements. In this paper, seven new infinite classes of optimal (v, {3, 4, 6}, 1,Q)-OOCs are constructed.
Yan LIU , Dianhua WU . Constructions of optimal variable-weight OOCs via quadratic residues[J]. Frontiers of Mathematics in China, 2013 , 8(4) : 869 -890 . DOI: 10.1007/s11464-012-0220-7
| 1 |
Abel R J R, Buratti M. Some progress on (v, 4, 1) difference families and optical orthogonal codes. J Combin Theory, 2004, 106: 59-75
|
| 2 |
Bitan S, Etzion T. Constructions for optimal constant weight cyclically permutable codes and difference families. IEEE Trans Inform Theory, 1995, 41: 77-87
|
| 3 |
Brickell E F, Wei V. Optical orthogonal codes and cyclic block designs. Congr Numer, 1987, 58: 175-182
|
| 4 |
Buratti M. Recursive constructions for difference matrices and relative difference families. J Combin Des, 1988, 6: 165-182
|
| 5 |
Buratti M. Pairwise balanced designs from finite fields. Discrete Math, 1999, 208/209: 103-117
|
| 6 |
Buratti M. Old and new designs via strong difference families. J Combin Des, 1999, 7: 406-425
|
| 7 |
Buratti M. On point-regular linear spaces. J Statist Plann Inference, 2001, 94: 139-146
|
| 8 |
Buratti M. Cyclic designs with block size 4 and related optimal optical orthogonal codes. Des Codes Cryptogr, 2002, 26: 111-125
|
| 9 |
Buratti M, Gionfriddo L. Strong difference families over arbitrary graphs. J Combin Des, 2008, 16: 443-461
|
| 10 |
Buratti M, Pasotti A. Graph decompositions with the use of difference matrices. Bull Inst Combin Appl, 2006, 47: 23-32
|
| 11 |
Buratti M, Wei Y, Wu D, Fan P, Cheng M. Relative difference families with variable block sizes and their related OOCs. IEEE Trans Inform Theory, 2011, 57: 7489-7497
|
| 12 |
Chang Y, Fuji-Hara R, Miao Y. Combinatorial constructions of optimal optical orthogonal codes with weight 4. IEEE Trans Inform Theory, 2003, 49: 1283-1292
|
| 13 |
Chang Y, Ji L. Optimal (4up, 5, 1) optical orthogonal codes. J Combin Des, 2004, 12: 346-361
|
| 14 |
Chang Y, Miao Y. Constructions for optimal optical orthogonal codes. Discrete Math, 2003, 261: 127-139
|
| 15 |
Chen K, Ge G, Zhu L. Starters and related codes. J Statist Plann Inference, 2000, 86: 379-395
|
| 16 |
Chen K, Zhu L. Existence of (q, 6, 1) difference families with qa prime power. Des Codes Cryptogr, 1998, 15: 167-174
|
| 17 |
Chu W, Colbourn C J. Recursive constructions for optimal (n, 4, 2)-OOCs. J Combin Des, 2004, 12: 333-345
|
| 18 |
Chu W, Golomb S W. A new recursive construction for optical orthogonal codes. IEEE Trans Inform Theory, 2003, 49: 3072-3076
|
| 19 |
Chung F R K, Salehi J A, Wei V K. Optical orthogonal codes: Design, analysis, and applications. IEEE Trans Inform Theory, 1989, 35: 595-604
|
| 20 |
Chung H, Kumar P V. Optical orthogonal codes-new bounds and an optimal construction. IEEE Trans Inform Theory, 1990, 36: 866-873
|
| 21 |
Fuji-Hara F, Miao Y. Optical orthogonal codes: Their bounds and new optimal constructions. IEEE Trans Inform Theory, 2000, 46: 2396-2406
|
| 22 |
Fuji-Hara F, Miao Y, Yin J. Optimal (9v, 4, 1) optical orthogonal codes. SIAM J Discrete Math, 2001, 14: 256-266
|
| 23 |
Ge G, Yin J. Constructions for optimal (v, 4, 1) optical orthogonal codes. IEEE Trans Inform Theory, 2001, 47: 2998-3004
|
| 24 |
Golomb S W. Digital Communication with Space Application. Los Altos: Penisula, 1982
|
| 25 |
Gu F R, Wu J. Construction and performance analysis of variable-weight optical orthogonal codes for asynchronous optical CDMA systems. J Lightw Technol, 2005, 23: 740-748
|
| 26 |
Jiang J, Wu D, Fan P. General constructions of optimal variable-weight optical orthogonal codes. IEEE Trans Inform Theory, 2011, 7: 4488-4496
|
| 27 |
Ma S, Chang Y. A new class of optimal optical orthogonal codes with weight five. IEEE Trans Inform Theory, 2004, 50: 1848-1850
|
| 28 |
Ma S, Chang Y. Constructions of optimal optical orthogonal codes with weight five. J Combin Des, 2005, 13: 54-69
|
| 29 |
Massey J L, Mathys P. The collision channel without feedback. IEEE Trans Inform Theory, 1985, 31: 192-204
|
| 30 |
Mishima M, Fu H L, Uruno S. Optimal conflict-avoiding codes of length n ≡ 0 (mod 16) and weight 3. Des Codes Cryptogr, 2009, 52: 275-291
|
| 31 |
Momihara K. Necessary and sufficient conditions for tight equi-difference conflict avoiding codes of weight three. Des Codes Cryptogr, 2007, 45: 379-390
|
| 32 |
Momihara K. On cyclic 2(k-1)-support (n, k)k-1 difference families. Finite Fields Appl, 2009, 15: 415-427
|
| 33 |
Momihara K. Strong difference families, difference covers, and their applications for relative difference families. Des Codes Cryptogr, 2009, 51: 253-273
|
| 34 |
Momihara K. New optimal optical orthogonal codes by restrictions to subgroups. Finite Fields Appl, 2011, 17: 166-182
|
| 35 |
Momihara K, Buratti M. Bounds and constructions of optimal (n, 4, 2, 1) optical orthogonal codes. IEEE Trans Inform Theory, 2009, 55: 514-523
|
| 36 |
Momihara K, Müller M, Satoh J, Jimbo M. Constant weight conflict-avoiding codes. SIAM J Discrete Math, 2007, 21: 959-979
|
| 37 |
Salehi J A. Code division multiple access techniques in optical fiber networks—Part I Fundamental principles. IEEE Trans Commun, 1989, 37: 824-833
|
| 38 |
Salehi J A. Emerging optical code-division multiple-access communications systems. IEEE Network, 1989, 3: 31-39
|
| 39 |
Salehi J A, Brackett C A. Code division multiple access techniques in optical fiber networks—Part II Systems performance analysis. IEEE Trans Commun, 1989, 37: 834-842
|
| 40 |
Vecchi M P, Salehi J A. Neuromorphic networks based on sparse optical orthogonal codes. In: Neural Information Processing Systems—Natural and Synthetic. New York: Amer Inst Phys, 1988, 814-823
|
| 41 |
Wu D, Fan P, Li H, Parampalli U. Optimal variable-weight optical orthogonal codes via cyclic difference families. In: Proc 2009 IEEE International Symposium on Information Theory ISIT’9, June 28-July 3. 2009, 448-452
|
| 42 |
Wu D, Zhao H, Fan P, Shinohara S. Optimal variable-weight optical orthogonal codes via difference packings. IEEE Trans Inform Theory, 2010, 56: 4053-4060
|
| 43 |
Yang G C. Variable weight optical orthogonal codes for CDMA networks with multiple performance requirements. GLOBECOM ’93, IEEE, 1993, 1: 488-492
|
| 44 |
Yang G C. Variable-weight optical orthogonal codes for CDMA networks with multiple performance requirements. IEEE Trans Commun, 1996, 44: 47-55
|
| 45 |
Yang G C, Fuja T E. Optical orthogonal codes with unequal auto- and cross-correlation constraints. IEEE Trans Inform Theory, 1995, 41: 96-106
|
| 46 |
Yin J. Some combinatorial constructions for optical orthogonal codes. Discrete Math, 1998, 185: 201-219
|
| 47 |
Zhao H, Wu D, Fan P. Construction of optimal variable-weight optical orthogonal codes. J Combin Des, 2010, 18: 274-291
|
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