Information on Result #1300595

Linear OA(4186, 65604, F4, 28) (dual of [65604, 65418, 29]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(4182, 65597, F4, 28) (dual of [65597, 65415, 29]-code), using
    • construction X applied to Ce(28) ⊂ Ce(20) [i] based on
      1. linear OA(4169, 65536, F4, 29) (dual of [65536, 65367, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
      2. linear OA(4121, 65536, F4, 21) (dual of [65536, 65415, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
      3. linear OA(413, 61, F4, 6) (dual of [61, 48, 7]-code), using
  2. linear OA(4182, 65600, F4, 26) (dual of [65600, 65418, 27]-code), using Gilbert–VarÅ¡amov bound and bm = 4182 > Vbs−1(k−1) = 143841 756290 016350 169662 786892 659721 213183 918115 845900 235006 828617 848740 709183 661310 225110 542099 256145 980430 [i]
  3. linear OA(41, 4, F4, 1) (dual of [4, 3, 2]-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(4186, 65604, F4, 2, 28) (dual of [(65604, 2), 131022, 29]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(4186, 65604, F4, 3, 28) (dual of [(65604, 3), 196626, 29]-NRT-code) [i]
3Digital (158, 186, 65604)-net over F4 [i]
4Linear OOA(4186, 32802, F4, 2, 28) (dual of [(32802, 2), 65418, 29]-NRT-code) [i]OOA Folding