The Classification of the Largest Caps in AG(5, 3)
نویسندگان
چکیده
We prove that 45 is the size of the largest caps in AG(5, 3), and such a 45-cap is always obtained from the 56-cap in PG(5, 3) by deleting an 11-hyperplane.
منابع مشابه
Caps and Colouring Steiner Triple Systems
Hill [6] showed that the largest cap in PG(5, 3) has cardinality 56. Using this cap it is easy to construct a cap of cardinality 45 in AG(5, 3). Here we show that the size of a cap in AG(5, 3) is bounded above by 48. We also give an example of three disjoint 45-caps in AG(5, 3). Using these two results we are able to prove that the Steiner triple system AG(5, 3) is 6-chromatic, and so we exhibi...
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ورودعنوان ژورنال:
- J. Comb. Theory, Ser. A
دوره 99 شماره
صفحات -
تاریخ انتشار 2002