Information on Result #1302206

Linear OA(781, 16829, F7, 18) (dual of [16829, 16748, 19]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(779, 16825, F7, 18) (dual of [16825, 16746, 19]-code), using
    • construction X applied to Ce(17) ⊂ Ce(14) [i] based on
      1. linear OA(776, 16807, F7, 18) (dual of [16807, 16731, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
      2. linear OA(761, 16807, F7, 15) (dual of [16807, 16746, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
      3. linear OA(73, 18, F7, 2) (dual of [18, 15, 3]-code), using
  2. linear OA(779, 16827, F7, 17) (dual of [16827, 16748, 18]-code), using Gilbert–VarÅ¡amov bound and bm = 779 > Vbs−1(k−1) = 5 526691 201027 221273 520674 281865 416501 062589 608660 314170 504173 055857 [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(781, 16829, F7, 2, 18) (dual of [(16829, 2), 33577, 19]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(781, 16829, F7, 3, 18) (dual of [(16829, 3), 50406, 19]-NRT-code) [i]
3Digital (63, 81, 16829)-net over F7 [i]