Information on Result #1300047

Linear OA(4112, 16435, F4, 19) (dual of [16435, 16323, 20]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(4109, 16429, F4, 19) (dual of [16429, 16320, 20]-code), using
    • construction X applied to Ce(18) ⊂ Ce(12) [i] based on
      1. linear OA(499, 16384, F4, 19) (dual of [16384, 16285, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
      2. linear OA(464, 16384, F4, 13) (dual of [16384, 16320, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
      3. linear OA(410, 45, F4, 5) (dual of [45, 35, 6]-code), using
  2. linear OA(4109, 16432, F4, 18) (dual of [16432, 16323, 19]-code), using Gilbert–VarÅ¡amov bound and bm = 4109 > Vbs−1(k−1) = 167045 512173 122570 211427 209547 427698 666304 509520 235721 042496 871916 [i]
  3. linear OA(40, 3, F4, 0) (dual of [3, 3, 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(4112, 16435, F4, 2, 19) (dual of [(16435, 2), 32758, 20]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(4112, 16435, F4, 3, 19) (dual of [(16435, 3), 49193, 20]-NRT-code) [i]
3Digital (93, 112, 16435)-net over F4 [i]
4Linear OOA(4112, 8217, F4, 2, 19) (dual of [(8217, 2), 16322, 20]-NRT-code) [i]OOA Folding