Information on Result #1300327

Linear OA(4156, 262193, F4, 22) (dual of [262193, 262037, 23]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(4152, 262187, F4, 22) (dual of [262187, 262035, 23]-code), using
    • construction X applied to Ce(21) ⊂ Ce(16) [i] based on
      1. linear OA(4145, 262144, F4, 22) (dual of [262144, 261999, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
      2. linear OA(4109, 262144, F4, 17) (dual of [262144, 262035, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
      3. linear OA(47, 43, F4, 4) (dual of [43, 36, 5]-code), using
  2. linear OA(4152, 262189, F4, 19) (dual of [262189, 262037, 20]-code), using Gilbert–VarÅ¡amov bound and bm = 4152 > Vbs−1(k−1) = 2 073140 130308 252451 203559 837483 958671 321221 068454 777134 762413 288439 014062 930148 128428 833934 [i]
  3. linear OA(42, 4, F4, 2) (dual of [4, 2, 3]-code or 4-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(4156, 131096, F4, 2, 22) (dual of [(131096, 2), 262036, 23]-NRT-code) [i]OOA Folding