Information on Result #1297867

Linear OA(339, 19705, F3, 6) (dual of [19705, 19666, 7]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(338, 19703, F3, 6) (dual of [19703, 19665, 7]-code), using
    • construction X4 applied to Ce(6) ⊂ Ce(3) [i] based on
      1. linear OA(337, 19683, F3, 7) (dual of [19683, 19646, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
      2. linear OA(319, 19683, F3, 4) (dual of [19683, 19664, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
      3. linear OA(319, 20, F3, 19) (dual of [20, 1, 20]-code or 20-arc in PG(18,3)), using
      4. linear OA(31, 20, F3, 1) (dual of [20, 19, 2]-code), using
  2. linear OA(338, 19704, F3, 5) (dual of [19704, 19666, 6]-code), using Gilbert–VarÅ¡amov bound and bm = 338 > Vbs−1(k−1) = 100450 014116 830827 [i]
  3. linear OA(30, 1, F3, 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(339, 19705, F3, 2, 6) (dual of [(19705, 2), 39371, 7]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(339, 19705, F3, 3, 6) (dual of [(19705, 3), 59076, 7]-NRT-code) [i]
3Linear OOA(339, 19705, F3, 4, 6) (dual of [(19705, 4), 78781, 7]-NRT-code) [i]
4Linear OOA(339, 19705, F3, 5, 6) (dual of [(19705, 5), 98486, 7]-NRT-code) [i]