Information on Result #1302232

Linear OA(786, 16834, F7, 19) (dual of [16834, 16748, 20]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(785, 16832, F7, 19) (dual of [16832, 16747, 20]-code), using
    • construction X applied to C([0,9]) ⊂ C([0,7]) [i] based on
      1. linear OA(781, 16808, F7, 19) (dual of [16808, 16727, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 16808 | 710−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
      2. linear OA(761, 16808, F7, 15) (dual of [16808, 16747, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 16808 | 710−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
      3. linear OA(74, 24, F7, 3) (dual of [24, 20, 4]-code or 24-cap in PG(3,7)), using
  2. linear OA(785, 16833, F7, 18) (dual of [16833, 16748, 19]-code), using Gilbert–VarÅ¡amov bound and bm = 785 > Vbs−1(k−1) = 32989 294105 206223 001405 174883 080732 242307 607219 744237 045160 634340 751873 [i]
  3. linear OA(70, 1, F7, 0) (dual of [1, 1, 1]-code), using

Mode: 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 OOA(786, 16834, F7, 2, 19) (dual of [(16834, 2), 33582, 20]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(786, 16834, F7, 3, 19) (dual of [(16834, 3), 50416, 20]-NRT-code) [i]
3Digital (67, 86, 16834)-net over F7 [i]
4Linear OOA(786, 8417, F7, 2, 19) (dual of [(8417, 2), 16748, 20]-NRT-code) [i]OOA Folding