Bounds on affine caps

  title={Bounds on affine caps},
  author={J{\"u}rgen Bierbrauer},
A cap in affine space AG(k, q) is a set A of k-tuples in IF k q such that whenever a1, a2, a3 are different elements of A and λi ∈ IFq, i = 1, 2, 3 such that (λ1, λ2, λ3) 6= (0, 0, 0) and λ1 + λ2 + λ3 = 0, we have ∑3 i=1 λiai 6= 0. An equivalent condition is that any three of the (k +1)-tuples (ai, 1) are linearly independent. Denote by Ck(q) the maximum cardinality of a cap in AG(k, q), and ck(q) = Ck(q)/q . Clearly ck(2) = 1. Henceforth we assume q > 2. The values Ck(q) for k ≤ 3 are well… CONTINUE READING
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