Information on Result #1301037

Linear OA(4238, 262194, F4, 34) (dual of [262194, 261956, 35]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(4233, 262187, F4, 34) (dual of [262187, 261954, 35]-code), using
    • construction X applied to Ce(33) ⊂ Ce(28) [i] based on
      1. linear OA(4226, 262144, F4, 34) (dual of [262144, 261918, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
      2. linear OA(4190, 262144, F4, 29) (dual of [262144, 261954, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
      3. linear OA(47, 43, F4, 4) (dual of [43, 36, 5]-code), using
  2. linear OA(4233, 262189, F4, 30) (dual of [262189, 261956, 31]-code), using Gilbert–VarÅ¡amov bound and bm = 4233 > Vbs−1(k−1) = 106 928274 624300 632029 266137 965055 670011 818578 575135 555967 739058 358921 101556 229258 080753 168507 902376 417127 845917 384571 160622 578402 473443 834008 [i]
  3. linear OA(43, 5, F4, 3) (dual of [5, 2, 4]-code or 5-arc in PG(2,4) or 5-cap in PG(2,4)), 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(4238, 131097, F4, 2, 34) (dual of [(131097, 2), 261956, 35]-NRT-code) [i]OOA Folding
2Linear OOA(4238, 87398, F4, 3, 34) (dual of [(87398, 3), 261956, 35]-NRT-code) [i]