Information on Result #1302213

Linear OA(782, 117690, F7, 15) (dual of [117690, 117608, 16]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(780, 117686, F7, 15) (dual of [117686, 117606, 16]-code), using
    • construction X applied to Ce(14) ⊂ Ce(8) [i] based on
      1. linear OA(773, 117649, F7, 15) (dual of [117649, 117576, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 117648 = 76−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
      2. linear OA(743, 117649, F7, 9) (dual of [117649, 117606, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 117648 = 76−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
      3. linear OA(77, 37, F7, 5) (dual of [37, 30, 6]-code), using
  2. linear OA(780, 117688, F7, 14) (dual of [117688, 117608, 15]-code), using Gilbert–VarÅ¡amov bound and bm = 780 > Vbs−1(k−1) = 1 741311 565014 245928 585556 903158 309889 306255 037399 184975 583745 196151 [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(782, 117690, F7, 2, 15) (dual of [(117690, 2), 235298, 16]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(782, 117690, F7, 3, 15) (dual of [(117690, 3), 352988, 16]-NRT-code) [i]
3Digital (67, 82, 117690)-net over F7 [i]
4Linear OOA(782, 58845, F7, 2, 15) (dual of [(58845, 2), 117608, 16]-NRT-code) [i]OOA Folding