Information on Result #1297278

Linear OA(2149, 305, F2, 36) (dual of [305, 156, 37]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(2146, 301, F2, 36) (dual of [301, 155, 37]-code), using
    • 1 times truncation [i] based on linear OA(2147, 302, F2, 37) (dual of [302, 155, 38]-code), using
      • construction X applied to Ce(36) ⊂ Ce(26) [i] based on
        1. linear OA(2125, 256, F2, 37) (dual of [256, 131, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
        2. linear OA(2101, 256, F2, 27) (dual of [256, 155, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
        3. linear OA(222, 46, F2, 9) (dual of [46, 24, 10]-code), using
  2. linear OA(2146, 302, F2, 33) (dual of [302, 156, 34]-code), using Gilbert–VarÅ¡amov bound and bm = 2146 > Vbs−1(k−1) = 16 086667 052622 603144 229988 702158 058507 823741 [i]
  3. linear OA(22, 3, F2, 2) (dual of [3, 1, 3]-code or 3-arc in PG(1,2)), 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 OA(2150, 306, F2, 37) (dual of [306, 156, 38]-code) [i]Adding a Parity Check Bit