Information on Result #691623

Linear OA(1684, 1048594, F16, 18) (dual of [1048594, 1048510, 19]-code), using construction X applied to Ce(17) ⊂ Ce(13) based on
  1. linear OA(1681, 1048576, F16, 18) (dual of [1048576, 1048495, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
  2. linear OA(1666, 1048576, F16, 14) (dual of [1048576, 1048510, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
  3. linear OA(163, 18, F16, 3) (dual of [18, 15, 4]-code or 18-arc in PG(2,16) or 18-cap in PG(2,16)), using

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

ResultThis
result
only		Method
1Linear OA(1685, 1048595, F16, 18) (dual of [1048595, 1048510, 19]-code) [i]Code Embedding in Larger Space
2Linear OOA(1684, 799495, F16, 2, 18) (dual of [(799495, 2), 1598906, 19]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
3Digital (66, 84, 799495)-net over F16 [i]
4Linear OOA(1684, 524297, F16, 2, 18) (dual of [(524297, 2), 1048510, 19]-NRT-code) [i]OOA Folding
5Linear OOA(1684, 116510, F16, 18, 18) (dual of [(116510, 18), 2097096, 19]-NRT-code) [i]OA Folding and Stacking