Information on Result #1300043

Linear OA(4110, 16431, F4, 19) (dual of [16431, 16321, 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, 16430, F4, 18) (dual of [16430, 16321, 19]-code), using Gilbert–VarÅ¡amov bound and bm = 4109 > Vbs−1(k−1) = 166700 027010 536656 823869 781104 264101 530933 870761 148571 702420 458896 [i]
  3. linear OA(40, 1, F4, 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(4110, 16431, F4, 2, 19) (dual of [(16431, 2), 32752, 20]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(4110, 16431, F4, 3, 19) (dual of [(16431, 3), 49183, 20]-NRT-code) [i]
3Digital (91, 110, 16431)-net over F4 [i]