New construction of projective planes of prime order

Abstract

Abstract:

The existence of projective plane which consists of Euclidean plane and an extrinsic straight line is an important research subject in projective geometry. There is a close connection between affine plane and projective plane in combinatorial design. A projective plane of order q corresponds to a (q2+q+1,q+1,1)symmetrical design,and an affine plane of order q corresponds to a(q2,q,1)resolvable design. Beginning with infinity element and projective line,the definition of projective plane is given. Furthermore,the elementary transformation of matrix and the position transformation of the diagonal elements are used to get the parallel classes of a resolvable design. Finally,a new construction of projective plane of prime order is obtained by adding q+1 points into each parallel class. The correctness and efficiency of the construction are validated through an example.

Key words: projective plane, affine plane, design, matrix

CLC Number:

O157

CHEN Shang-di,WEI Hui-hui. New construction of projective planes of prime order[J]. .

[1]	GAO Y ou, , XIE Mingyue , WANG Gang. New constructions of optimal and asymptotically optimal codebooks [J]. Journal of Civil Aviation University of China, 2026, 44(1): 86-90.
[2]	SHU Juncheng, , HE Erming, , YIN Menghan, , ZHAO Guanchen, . Progress on civil aircraft vibration comfort design [J]. Journal of Civil Aviation University of China, 2025, 43(2): 1-7.
[3]	DING Xinwei , QIN Qian, KAN Ben , LIU Qichang, JIA Chi . Prediction of spatiotemporal distribution of passenger flow in terminal building based on graph convolutional neural network#br# [J]. Journal of Civil Aviation University of China, 2023, 41(6): 31-36.
[4]	YANG Jianzhong, CHEN Bang, SUN Xiaozhe. Design of the flaps actuation system architecture based on design structure matrix [J]. Journal of Civil Aviation University of China, 2022, 40(3): 59-64.
[5]	LIU Haohan, MA Xiaolu, HE Huaiqing. Top-N recommendation algorithm based on user’s interest drift [J]. Journal of Civil Aviation University of China, 2021, 39(3): 56-61.
[6]	CAO Huiling, ZHENG Lijiu. Nonlinear steady state control of small turbofan engine based on LMI [J]. Journal of Civil Aviation University of China, 2020, 38(3): 12-17.
[7]	SU Jingxin, ZHAO Wenhao, CHEN Dong, LU Pengcheng. Flexural properties of repaired composite laminate structure under hygrothermal conditions [J]. Journal of Civil Aviation University of China, 2020, 38(2): 60-64.
[8]	YANG Jingfeng, LI Changfu. Synchronous acquiring system design of multimodal finger image#br# [J]. Journal of Civil Aviation University of China, 2020, 38(1): 54-59.
[9]	ZHANG Xiwu, LI Zhiping, LI Yuekai. Risk assessment of civil aviation information system based on AHP and D-S evidence theory#br# [J]. Journal of Civil Aviation University of China, 2019, 37(4): 41-45.
[10]	. Design of deformable tracked robot [J]. , 2018, 36(6): 59-64.
[11]	XIE Chunsheng, DAI Yujie. OEI missed approach emergency procedure optimization based on PEP [J]. , 2018, 36(3): 7-10.
[12]	LI Hai, ZHAN Lei, WU Renbiao. Turbulence spectral width estimation method based on space-time covariance matrix fitting [J]. , 2018, 36(1): 20-24.
[13]	HU Tieqiao, ZHANG Maomao, LI Yangbo. FPGA implementation of matrix inversion based on configurable Cholesky decomposition [J]. , 2017, 35(4): 7-10,15.
[14]	XU Jianxin, YU Yiliang, MA Chao. Evaluation of civil aircraft out field information-delivery workflow system [J]. , 2017, 35(3): 9-12.
[15]	FEI Chunguo, WANG Shuai, HU Jiangyu. Design of airport vehicle monitoring system based on Android [J]. , 2017, 35(2): 34-40.

New construction of projective planes of prime order

Knowledge

Abstract

Cite this article

share this article

References

Related Articles 15

Recommended Articles

Metrics

Comments