Information on Result #1302186

Linear OA(777, 823579, F7, 12) (dual of [823579, 823502, 13]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(775, 823575, F7, 12) (dual of [823575, 823500, 13]-code), using
    • construction X applied to Ce(11) ⊂ Ce(7) [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(743, 823543, F7, 8) (dual of [823543, 823500, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 823542 = 77−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
      3. linear OA(74, 32, F7, 3) (dual of [32, 28, 4]-code or 32-cap in PG(3,7)), using
  2. linear OA(775, 823577, F7, 11) (dual of [823577, 823502, 12]-code), using Gilbert–VarÅ¡amov bound and bm = 775 > Vbs−1(k−1) = 2 392012 488029 206879 658599 954080 943155 411035 176907 714533 502017 [i]
  3. linear OA(70, 2, F7, 0) (dual of [2, 2, 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(777, 823579, F7, 2, 12) (dual of [(823579, 2), 1647081, 13]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(777, 823579, F7, 3, 12) (dual of [(823579, 3), 2470660, 13]-NRT-code) [i]
3Digital (65, 77, 823579)-net over F7 [i]
4Linear OOA(777, 411789, F7, 2, 12) (dual of [(411789, 2), 823501, 13]-NRT-code) [i]OOA Folding