Information on Result #1302168

Linear OA(773, 823561, F7, 12) (dual of [823561, 823488, 13]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(772, 823559, F7, 12) (dual of [823559, 823487, 13]-code), using
    • construction X4 applied to Ce(11) ⊂ Ce(9) [i] based on
      1. linear OA(771, 823543, F7, 12) (dual of [823543, 823472, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 823542 = 77−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
      2. linear OA(757, 823543, F7, 10) (dual of [823543, 823486, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 823542 = 77−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
      3. linear OA(715, 16, F7, 15) (dual of [16, 1, 16]-code or 16-arc in PG(14,7)), using
      4. linear OA(71, 16, F7, 1) (dual of [16, 15, 2]-code), using
  2. linear OA(772, 823560, F7, 11) (dual of [823560, 823488, 12]-code), using Gilbert–VarÅ¡amov bound and bm = 772 > Vbs−1(k−1) = 2 391518 779504 139374 297788 919597 266944 778868 777595 476355 021047 [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(773, 823561, F7, 2, 12) (dual of [(823561, 2), 1647049, 13]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(773, 823561, F7, 3, 12) (dual of [(823561, 3), 2470610, 13]-NRT-code) [i]
3Digital (61, 73, 823561)-net over F7 [i]