Information on Result #1302128

Linear OA(767, 117681, F7, 12) (dual of [117681, 117614, 13]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(765, 117677, F7, 12) (dual of [117677, 117612, 13]-code), using
    • construction X applied to Ce(11) ⊂ Ce(7) [i] based on
      1. linear OA(761, 117649, F7, 12) (dual of [117649, 117588, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 117648 = 76−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
      2. linear OA(737, 117649, F7, 8) (dual of [117649, 117612, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 117648 = 76−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
      3. linear OA(74, 28, F7, 3) (dual of [28, 24, 4]-code or 28-cap in PG(3,7)), using
  2. linear OA(765, 117679, F7, 11) (dual of [117679, 117614, 12]-code), using Gilbert–VarÅ¡amov bound and bm = 765 > Vbs−1(k−1) = 8482 860616 671076 086097 826866 924808 270876 233137 478993 [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(767, 117681, F7, 2, 12) (dual of [(117681, 2), 235295, 13]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(767, 117681, F7, 3, 12) (dual of [(117681, 3), 352976, 13]-NRT-code) [i]
3Digital (55, 67, 117681)-net over F7 [i]