Information on Result #1302134

Linear OA(767, 5764821, F7, 10) (dual of [5764821, 5764754, 11]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(766, 5764819, F7, 10) (dual of [5764819, 5764753, 11]-code), using
    • construction X4 applied to Ce(9) ⊂ Ce(7) [i] based on
      1. 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]
      2. linear OA(749, 5764801, F7, 8) (dual of [5764801, 5764752, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 78−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [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(766, 5764820, F7, 9) (dual of [5764820, 5764754, 10]-code), using Gilbert–VarÅ¡amov bound and bm = 766 > Vbs−1(k−1) = 50 812771 086022 967893 912537 396962 810040 553914 071512 474071 [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(767, 5764821, F7, 2, 10) (dual of [(5764821, 2), 11529575, 11]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(767, 5764821, F7, 3, 10) (dual of [(5764821, 3), 17294396, 11]-NRT-code) [i]
3Digital (57, 67, 5764821)-net over F7 [i]