Information on Result #1303872

Linear OA(27107, 19712, F27, 35) (dual of [19712, 19605, 36]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(27106, 19710, F27, 35) (dual of [19710, 19604, 36]-code), using
    • construction X applied to Ce(34) ⊂ Ce(27) [i] based on
      1. linear OA(27100, 19683, F27, 35) (dual of [19683, 19583, 36]-code), using an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
      2. linear OA(2779, 19683, F27, 28) (dual of [19683, 19604, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
      3. linear OA(276, 27, F27, 6) (dual of [27, 21, 7]-code or 27-arc in PG(5,27)), using
  2. linear OA(27106, 19711, F27, 34) (dual of [19711, 19605, 35]-code), using Gilbert–VarÅ¡amov bound and bm = 27106 > Vbs−1(k−1) = 29 409046 364641 841945 244859 900365 676700 692681 818486 406396 634889 030048 862167 282526 834453 154890 244771 074469 736033 606665 928641 651853 541413 709995 851721 501033 [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(27107, 19712, F27, 2, 35) (dual of [(19712, 2), 39317, 36]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Digital (72, 107, 19712)-net over F27 [i]
3Linear OOA(27107, 9856, F27, 2, 35) (dual of [(9856, 2), 19605, 36]-NRT-code) [i]OOA Folding