Information on Result #1300745

Linear OA(4202, 16432, F4, 36) (dual of [16432, 16230, 37]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(4200, 16429, F4, 36) (dual of [16429, 16229, 37]-code), using
    • construction X applied to Ce(36) ⊂ Ce(29) [i] based on
      1. linear OA(4190, 16384, F4, 37) (dual of [16384, 16194, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
      2. linear OA(4155, 16384, F4, 30) (dual of [16384, 16229, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
      3. linear OA(410, 45, F4, 5) (dual of [45, 35, 6]-code), using
  2. linear OA(4200, 16430, F4, 34) (dual of [16430, 16230, 35]-code), using Gilbert–VarÅ¡amov bound and bm = 4200 > Vbs−1(k−1) = 8087 377968 601659 308077 150898 922725 002754 841924 085541 173584 973493 331627 267636 470515 138416 706201 965756 343333 548226 218472 [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(4202, 8216, F4, 2, 36) (dual of [(8216, 2), 16230, 37]-NRT-code) [i]OOA Folding