Small complete arcs in Galois planes |
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Authors: | Tamás Sz?nyi |
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Institution: | 1. Computer and Automation Institute, Hungarian Academy of Sciences, P.O. Box 63, H-1502, Budapest, Hungary
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Abstract: | In this paper we construct a class of k-arcs in PG(2, q), q=p h, h>1, p≠3 and prove its completeness for h large enough. The main result states that this class contains complete k-arcs with $$k \leqslant 2 \cdot q^{{9 \mathord{\left/ {\vphantom {9 {10}}} \right. \kern-\nulldelimiterspace} {10}}} {\text{ }}\left( {10{\text{ divides }}h{\text{ and }}q{\text{ }} \geqslant {\text{ }}q_{\text{0}} } \right).$$ Such complete k-arcs are the unique known complete k-arcs with $$k \leqslant {q \mathord{\left/ {\vphantom {q 4}} \right. \kern-\nulldelimiterspace} 4}.$$ |
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