Information on Result #1300591

Linear OA(4184, 65600, F4, 28) (dual of [65600, 65416, 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, 65598, F4, 26) (dual of [65598, 65416, 27]-code), using Gilbert–VarÅ¡amov bound and bm = 4182 > Vbs−1(k−1) = 143732 139747 102926 774411 989123 874368 652564 275027 980087 151228 129207 313852 855833 315005 043453 018024 050916 713640 [i]
  3. linear OA(41, 2, F4, 1) (dual of [2, 1, 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(4184, 32800, F4, 2, 28) (dual of [(32800, 2), 65416, 29]-NRT-code) [i]OOA Folding