Information on Result #1300713

Linear OA(4198, 65590, F4, 31) (dual of [65590, 65392, 32]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(4195, 65586, F4, 31) (dual of [65586, 65391, 32]-code), using
    • construction X applied to Ce(30) ⊂ Ce(24) [i] based on
      1. linear OA(4185, 65536, F4, 31) (dual of [65536, 65351, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
      2. linear OA(4145, 65536, F4, 25) (dual of [65536, 65391, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
      3. linear OA(410, 50, F4, 5) (dual of [50, 40, 6]-code), using
  2. linear OA(4195, 65587, F4, 28) (dual of [65587, 65392, 29]-code), using Gilbert–VarÅ¡amov bound and bm = 4195 > Vbs−1(k−1) = 7 887276 516010 682566 501649 815728 422221 464089 546742 491652 892381 095349 142565 275619 190487 082739 578873 111706 314812 772880 [i]
  3. linear OA(42, 3, F4, 2) (dual of [3, 1, 3]-code or 3-arc in PG(1,4)), 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(4198, 32795, F4, 2, 31) (dual of [(32795, 2), 65392, 32]-NRT-code) [i]OOA Folding