Information on Result #1302027

Linear OA(748, 16821, F7, 11) (dual of [16821, 16773, 12]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(747, 16819, F7, 11) (dual of [16819, 16772, 12]-code), using
    • construction X4 applied to Ce(10) ⊂ Ce(8) [i] based on
      1. linear OA(746, 16807, F7, 11) (dual of [16807, 16761, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
      2. linear OA(736, 16807, F7, 9) (dual of [16807, 16771, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
      3. linear OA(711, 12, F7, 11) (dual of [12, 1, 12]-code or 12-arc in PG(10,7)), using
      4. linear OA(71, 12, F7, 1) (dual of [12, 11, 2]-code), using
  2. linear OA(747, 16820, F7, 10) (dual of [16820, 16773, 11]-code), using Gilbert–VarÅ¡amov bound and bm = 747 > Vbs−1(k−1) = 2984 755571 977452 274395 337031 019568 277719 [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(748, 16821, F7, 2, 11) (dual of [(16821, 2), 33594, 12]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(748, 16821, F7, 3, 11) (dual of [(16821, 3), 50415, 12]-NRT-code) [i]
3Digital (37, 48, 16821)-net over F7 [i]