型为tr的5-半循环可分组设计
Semi-Cyclic Group Divisible Design of Type tr with Block Size 5
DOI: 10.12677/PM.2024.141034, PDF,    国家自然科学基金支持
作者: 杜 珺：内蒙古师范大学数学科学学院，内蒙古 呼和浩特；黄月梅*：内蒙古师范大学数学科学学院，内蒙古 呼和浩特；内蒙古自治区应用数学中心，内蒙古 呼和浩特
关键词: 半循环可分组设计；循环差阵；循环填充；递归构造；Semi-Cyclic Group Divisible Design； Cyclic Difference Matrix； Cyclic Packing； Recursive Construction
摘要: 半循环可分组设计在组合编码中有着广泛的应用。根据半循环可分组设计的定义，给出型为tr，区组长度为5的半循环可分组设计存在的必要条件。再利用循环差阵、t-正则的循环填充及两种递归构造法，得到了型为tr，区组长度为5的半循环可分组设计存在的若干充分条件。
Abstract: Semi-cyclic group divisible design has many applications in combinatorial coding. The necessary condition of semi-cyclic group divisible design of type tr with block size 5 was obtained from the definition. In addition, several spectrums of semi-cyclic group divisible design with block size 5 were obtained by employing cyclic difference matrix, t-regular cyclic packing with the aid of two recursive constructions.
文章引用：杜珺, 黄月梅. 型为tr的5-半循环可分组设计[J]. 理论数学, 2024, 14(1): 335-340. https://doi.org/10.12677/PM.2024.141034

参考文献

[1] Yin, J.X. (2002) A General Construction for Optimal Cyclic Packing Designs. Journal of Combinatorial Theory (Series A), 97, 272-284. [Google Scholar] [CrossRef] 
[2] Gallant, R.P., Jiang, Z. and Ling, A.C.H. (1999) The Spectrum of Cyclic Group Divisible Designs with Block Size Three. Journal of Combinatorial Design, 7, 95-105. [Google Scholar] [CrossRef] 
[3] Wang, J.M. and Yin, J.X. (2010) Two-Dimensional Optical Orthogonal Codes and Semicyclic Group Divisible Designs. IEEE Transactions on Information Theory, 56, 2177-2187. [Google Scholar] [CrossRef] 
[4] Wang, K. and Wang, J.M. (2012) Semicyclic 4-GDDs and Related Two-Dimensional Optical Orthogonal Codes. Designs, Codes and Cryptog-raphy, 63, 305-319. [Google Scholar] [CrossRef] 
[5] Wang, L.D., Feng, T., Li, Y.T., et al. (2023) Construction for Multichannel Conflict-Avoiding Codes with AM-OPPTS Restriction. IEEE Transactions on Infor-mation Theory, 69, 7398-7413. [Google Scholar] [CrossRef] 
[6] Ge, G.N. and Yin, J.X. (2001) Constructions for Optimal Optical Orthogonal Codes. IEEE Transactions on Information Theory, 47, 2998-3004. [Google Scholar] [CrossRef] 
[7] Hanani, H. (1975) Balanced Incomplete Block Designs and Related Designs. Discrete Mathematics, 11, 255-369. [Google Scholar] [CrossRef] 
[8] Pan, R., Abel, R.J.R., Bunjamin, Y.A., et al. (2022) Differ-ence Matrices with Five Rows over Finite Abelian Groups. Designs, Codes and Cryptography, 90, 367-386. [Google Scholar] [CrossRef] 
[9] Ge, G.N. (2005) On -Difference Matrices. Discrete Mathematics, 301, 164-174. [Google Scholar] [CrossRef] 
[10] Yin, J.X. (1998) Some Combinatorial Constructions for Optical Orthogonal Codes. Discrete Mathematics, 185, 201-219. [Google Scholar] [CrossRef] 
[11] Chang, Y.X. and Ji, L.J. (2004) Optimal Opti-cal Orthogonal Codes. Journal of Combinatorial Designs, 12, 346-361. [Google Scholar] [CrossRef] 
[12] Ma, S. and Chang, Y.X. (2004) A New Class of Optimal Optical Orthogonal Codes with Weight Five. IEEE Transactions on Information Theory, 50, 1848-1850. [Google Scholar] [CrossRef] 
[13] Ma, S. and Chang, Y.X. (2005) Constructions of Optimal Optical Orthogonal Codes with Weight Five. Journal of Combinatorial Designs, 13, 54-69. [Google Scholar] [CrossRef] 

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