Information on Result #1302225

Linear OA(783, 823577, F7, 13) (dual of [823577, 823494, 14]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(782, 823575, F7, 13) (dual of [823575, 823493, 14]-code), using
    • construction X applied to Ce(12) ⊂ Ce(8) [i] based on
      1. linear OA(778, 823543, F7, 13) (dual of [823543, 823465, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 823542 = 77−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
      2. linear OA(750, 823543, F7, 9) (dual of [823543, 823493, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 823542 = 77−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [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(782, 823576, F7, 12) (dual of [823576, 823494, 13]-code), using Gilbert–VarÅ¡amov bound and bm = 782 > Vbs−1(k−1) = 1 074520 496494 241139 277116 848866 162544 372433 609779 915809 701206 519671 [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, 823577, F7, 2, 13) (dual of [(823577, 2), 1647071, 14]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(783, 823577, F7, 3, 13) (dual of [(823577, 3), 2470648, 14]-NRT-code) [i]
3Digital (70, 83, 823577)-net over F7 [i]