Information on Result #1300982

Linear OA(4232, 65600, F4, 36) (dual of [65600, 65368, 37]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(4230, 65597, F4, 36) (dual of [65597, 65367, 37]-code), using
    • construction X applied to Ce(36) ⊂ Ce(28) [i] based on
      1. linear OA(4217, 65536, F4, 37) (dual of [65536, 65319, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
      2. 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]
      3. linear OA(413, 61, F4, 6) (dual of [61, 48, 7]-code), using
  2. linear OA(4230, 65598, F4, 34) (dual of [65598, 65368, 35]-code), using Gilbert–VarÅ¡amov bound and bm = 4230 > Vbs−1(k−1) = 575524 186152 875055 728161 377102 587901 624113 174495 657469 614775 195923 288323 890347 811711 580156 380338 410064 394852 301572 390502 245365 161929 523048 [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(4232, 32800, F4, 2, 36) (dual of [(32800, 2), 65368, 37]-NRT-code) [i]OOA Folding