Information on Result #1300557

Linear OA(4183, 262192, F4, 26) (dual of [262192, 262009, 27]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(4179, 262187, F4, 26) (dual of [262187, 262008, 27]-code), using
    • construction X applied to Ce(25) ⊂ Ce(20) [i] based on
      1. linear OA(4172, 262144, F4, 26) (dual of [262144, 261972, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
      2. linear OA(4136, 262144, F4, 21) (dual of [262144, 262008, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
      3. linear OA(47, 43, F4, 4) (dual of [43, 36, 5]-code), using
  2. linear OA(4179, 262188, F4, 22) (dual of [262188, 262009, 23]-code), using Gilbert–VarÅ¡amov bound and bm = 4179 > Vbs−1(k−1) = 126 386420 590567 319488 563416 867629 380332 842803 554034 935289 136131 014941 399659 198304 045441 815453 097815 818536 [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(4183, 131096, F4, 2, 26) (dual of [(131096, 2), 262009, 27]-NRT-code) [i]OOA Folding