Information on Result #1302227

Linear OA(783, 5764821, F7, 12) (dual of [5764821, 5764738, 13]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(782, 5764819, F7, 12) (dual of [5764819, 5764737, 13]-code), using
    • construction X4 applied to Ce(11) ⊂ Ce(9) [i] based on
      1. linear OA(781, 5764801, F7, 12) (dual of [5764801, 5764720, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 78−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
      2. linear OA(765, 5764801, F7, 10) (dual of [5764801, 5764736, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 78−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
      3. linear OA(717, 18, F7, 17) (dual of [18, 1, 18]-code or 18-arc in PG(16,7)), using
      4. linear OA(71, 18, F7, 1) (dual of [18, 17, 2]-code), using
  2. linear OA(782, 5764820, F7, 11) (dual of [5764820, 5764738, 12]-code), using Gilbert–VarÅ¡amov bound and bm = 782 > Vbs−1(k−1) = 675 465182 712931 841096 394325 003319 589709 251023 228919 659940 837312 665047 [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(783, 5764821, F7, 2, 12) (dual of [(5764821, 2), 11529559, 13]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(783, 5764821, F7, 3, 12) (dual of [(5764821, 3), 17294380, 13]-NRT-code) [i]
3Digital (71, 83, 5764821)-net over F7 [i]