Complete ( q 2 + q + 8 ) / 2 - caps in the projective space PG ( 3 , q ) with odd prime q ≡ 2 ( mod 3 )
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چکیده
Abstract. In the projective space PG(3, q) with odd prime q ≡ 2 (mod 3), q ≥ 11, a new infinite family of complete (q + q + 8)/2-caps is constructed. It gives a new lower bound on the second largest size m′2(3, q) of complete caps: (q 2 + q + 8)/2 ≤ m ′2(3, q). The structure of one of the two existing complete 20-caps in PG(3, 5) is described. The new upper bounds on the smallest size of complete caps in PG(3, q) are obtained for q = 13, 19, 23. Many new sizes of complete caps in PG(3, q) are obtained.
منابع مشابه
Complete ( q 2 + q + 8)/2-caps in the spaces PG (3, q ), q = 2 (mod 3) an odd prime, and a complete 20-cap in PG (3, 5)
An infinite family of complete (q2 + q + 8)/2-caps is constructed in PG(3, q) where q is an odd prime ≡ 2 (mod 3), q ≥ 11. This yields a new lower bound on the second largest size of complete caps. A variant of our construction also produces one of the two previously known complete 20-caps in PG(3, 5). The associated code weight distribution and other combinatorial properties of the new (q2 + q...
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تاریخ انتشار 2006