Information on Result #1302111

Linear OA(763, 117665, F7, 12) (dual of [117665, 117602, 13]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(762, 117663, F7, 12) (dual of [117663, 117601, 13]-code), using
    • construction X4 applied to Ce(11) ⊂ Ce(9) [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(749, 117649, F7, 10) (dual of [117649, 117600, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 117648 = 76−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
      3. linear OA(713, 14, F7, 13) (dual of [14, 1, 14]-code or 14-arc in PG(12,7)), using
      4. linear OA(71, 14, F7, 1) (dual of [14, 13, 2]-code), using
  2. linear OA(762, 117664, F7, 11) (dual of [117664, 117602, 12]-code), using Gilbert–VarÅ¡amov bound and bm = 762 > Vbs−1(k−1) = 8472 053615 529211 601175 623181 786999 689761 593867 423415 [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(763, 117665, F7, 2, 12) (dual of [(117665, 2), 235267, 13]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(763, 117665, F7, 3, 12) (dual of [(117665, 3), 352932, 13]-NRT-code) [i]
3Digital (51, 63, 117665)-net over F7 [i]