The maximal size of 6- and 7-arcs in projective Hjelmslev planes over chain rings of order 9 |
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| Authors: | Thomas Honold Michael Kiermaier |
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| Institution: | 1 Department of Information and Electronic Engineering,Zhejiang University,Hangzhou 310027,China;2 Mathematisches Institut,Universita¨t Bayreuth,D-95440 Bayreuth,Germany |
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| Abstract: | We complete the determination of the maximum sizes of (k,n)-arcs,n≤12,in the projective Hjelmslev planes over the two (proper) chain rings Z 9=Z/9Z and S 3=F 3 X]/(X 2) of order 9 by resolving the hitherto open cases n=6 and n=7.Parts of our proofs rely on decidedly geometric properties of the planes such as Desargues’ theorem and the existence of certain subplanes. |
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| Keywords: | Hjelmslev geometry projective Hjelmslev plane arc finite chain ring Galois ring subplane affine subplane |
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