Information on Result #1300811

Linear OA(4210, 262192, F4, 30) (dual of [262192, 261982, 31]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(4206, 262187, F4, 30) (dual of [262187, 261981, 31]-code), using
    • construction X applied to Ce(29) ⊂ Ce(24) [i] based on
      1. linear OA(4199, 262144, F4, 30) (dual of [262144, 261945, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
      2. linear OA(4163, 262144, F4, 25) (dual of [262144, 261981, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
      3. linear OA(47, 43, F4, 4) (dual of [43, 36, 5]-code), using
  2. linear OA(4206, 262188, F4, 26) (dual of [262188, 261982, 27]-code), using Gilbert–VarÅ¡amov bound and bm = 4206 > Vbs−1(k−1) = 159 287393 964220 607680 872033 943006 310297 023714 683955 988169 832027 720432 270910 051271 578753 000446 541581 165657 147429 995572 007652 [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(4210, 131096, F4, 2, 30) (dual of [(131096, 2), 261982, 31]-NRT-code) [i]OOA Folding