Information on Result #1303860

Linear OA(2793, 19713, F27, 30) (dual of [19713, 19620, 31]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(2792, 19711, F27, 30) (dual of [19711, 19619, 31]-code), using
    • construction X applied to Ce(29) ⊂ Ce(21) [i] based on
      1. linear OA(2785, 19683, F27, 30) (dual of [19683, 19598, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
      2. linear OA(2764, 19683, F27, 22) (dual of [19683, 19619, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
      3. linear OA(277, 28, F27, 7) (dual of [28, 21, 8]-code or 28-arc in PG(6,27)), using
  2. linear OA(2792, 19712, F27, 29) (dual of [19712, 19620, 30]-code), using Gilbert–VarÅ¡amov bound and bm = 2792 > Vbs−1(k−1) = 23913 696642 876181 423233 841026 328187 071540 992826 960651 191865 418059 955347 305690 456487 235153 323393 383536 560152 151905 500098 514082 536979 [i]
  3. linear OA(270, 1, F27, 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(2793, 19713, F27, 2, 30) (dual of [(19713, 2), 39333, 31]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Digital (63, 93, 19713)-net over F27 [i]