Information on Result #1303864

Linear OA(2799, 19713, F27, 32) (dual of [19713, 19614, 33]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(2798, 19711, F27, 32) (dual of [19711, 19613, 33]-code), using
    • construction X applied to Ce(31) ⊂ Ce(23) [i] based on
      1. linear OA(2791, 19683, F27, 32) (dual of [19683, 19592, 33]-code), using an extension Ce(31) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,31], and designed minimum distance d ≥ |I|+1 = 32 [i]
      2. linear OA(2770, 19683, F27, 24) (dual of [19683, 19613, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [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(2798, 19712, F27, 31) (dual of [19712, 19614, 32]-code), using Gilbert–VarÅ¡amov bound and bm = 2798 > Vbs−1(k−1) = 7 198406 679869 041837 572382 521555 846295 588279 085160 621733 054443 951455 143543 251559 082608 845486 737449 392426 033499 830864 471772 933625 018607 934995 [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(2799, 19713, F27, 2, 32) (dual of [(19713, 2), 39327, 33]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Digital (67, 99, 19713)-net over F27 [i]