Information on Result #1300219

Linear OA(4138, 16431, F4, 24) (dual of [16431, 16293, 25]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(4137, 16429, F4, 24) (dual of [16429, 16292, 25]-code), using
    • construction X applied to Ce(24) ⊂ Ce(17) [i] based on
      1. linear OA(4127, 16384, F4, 25) (dual of [16384, 16257, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
      2. linear OA(492, 16384, F4, 18) (dual of [16384, 16292, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
      3. linear OA(410, 45, F4, 5) (dual of [45, 35, 6]-code), using
  2. linear OA(4137, 16430, F4, 23) (dual of [16430, 16293, 24]-code), using Gilbert–VarÅ¡amov bound and bm = 4137 > Vbs−1(k−1) = 15255 657857 280173 740738 349388 552632 026673 955706 059433 198633 918126 604824 132532 693176 [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(4138, 16431, F4, 2, 24) (dual of [(16431, 2), 32724, 25]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(4138, 16431, F4, 3, 24) (dual of [(16431, 3), 49155, 25]-NRT-code) [i]
3Digital (114, 138, 16431)-net over F4 [i]