Information on Result #1302208

Linear OA(780, 823561, F7, 13) (dual of [823561, 823481, 14]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(779, 823559, F7, 13) (dual of [823559, 823480, 14]-code), using
    • construction X4 applied to Ce(12) ⊂ Ce(10) [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(764, 823543, F7, 11) (dual of [823543, 823479, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 823542 = 77−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [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(779, 823560, F7, 12) (dual of [823560, 823481, 13]-code), using Gilbert–VarÅ¡amov bound and bm = 779 > Vbs−1(k−1) = 1 074290 889782 162311 524754 763248 220837 953076 332077 124906 240848 722167 [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(780, 823561, F7, 2, 13) (dual of [(823561, 2), 1647042, 14]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(780, 823561, F7, 3, 13) (dual of [(823561, 3), 2470603, 14]-NRT-code) [i]
3Digital (67, 80, 823561)-net over F7 [i]