Information on Result #1302050

Linear OA(751, 117665, F7, 10) (dual of [117665, 117614, 11]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(750, 117663, F7, 10) (dual of [117663, 117613, 11]-code), using
    • construction X4 applied to Ce(9) ⊂ Ce(7) [i] based on
      1. 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]
      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(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(750, 117664, F7, 9) (dual of [117664, 117614, 10]-code), using Gilbert–VarÅ¡amov bound and bm = 750 > Vbs−1(k−1) = 1 530066 788930 745037 032465 850622 055257 307319 [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(751, 117665, F7, 2, 10) (dual of [(117665, 2), 235279, 11]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(751, 117665, F7, 3, 10) (dual of [(117665, 3), 352944, 11]-NRT-code) [i]
3Digital (41, 51, 117665)-net over F7 [i]