Information on Result #1300387

Linear OA(4162, 16441, F4, 28) (dual of [16441, 16279, 29]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(4161, 16439, F4, 28) (dual of [16439, 16278, 29]-code), using
    • construction X applied to Ce(28) ⊂ Ce(20) [i] based on
      1. linear OA(4148, 16384, F4, 29) (dual of [16384, 16236, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
      2. linear OA(4106, 16384, F4, 21) (dual of [16384, 16278, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
      3. linear OA(413, 55, F4, 6) (dual of [55, 42, 7]-code), using
  2. linear OA(4161, 16440, F4, 27) (dual of [16440, 16279, 28]-code), using Gilbert–VarÅ¡amov bound and bm = 4161 > Vbs−1(k−1) = 253473 623195 315634 881111 504064 189772 532525 068509 905644 918699 106368 238159 232919 363416 735410 177884 [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(4162, 16441, F4, 2, 28) (dual of [(16441, 2), 32720, 29]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(4162, 16441, F4, 3, 28) (dual of [(16441, 3), 49161, 29]-NRT-code) [i]
3Digital (134, 162, 16441)-net over F4 [i]