Information on Result #1301035

Linear OA(4237, 262192, F4, 34) (dual of [262192, 261955, 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, 262188, F4, 30) (dual of [262188, 261955, 31]-code), using Gilbert–VarÅ¡amov bound and bm = 4233 > Vbs−1(k−1) = 106 916447 553568 232487 569708 261590 553420 588532 883435 996397 531101 270331 908787 734003 283649 197642 380681 850499 396318 906452 123122 897911 162837 331792 [i]
  3. linear OA(43, 4, F4, 3) (dual of [4, 1, 4]-code or 4-arc in PG(2,4) or 4-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(4237, 131096, F4, 2, 34) (dual of [(131096, 2), 261955, 35]-NRT-code) [i]OOA Folding