Information on Result #1297611

Linear OA(2235, 577, F2, 50) (dual of [577, 342, 51]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(2232, 572, F2, 50) (dual of [572, 340, 51]-code), using
    • 1 times truncation [i] based on linear OA(2233, 573, F2, 51) (dual of [573, 340, 52]-code), using
      • construction X applied to Ce(50) ⊂ Ce(40) [i] based on
        1. linear OA(2208, 512, F2, 51) (dual of [512, 304, 52]-code), using an extension Ce(50) of the primitive narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [1,50], and designed minimum distance d ≥ |I|+1 = 51 [i]
        2. linear OA(2172, 512, F2, 41) (dual of [512, 340, 42]-code), using an extension Ce(40) of the primitive narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [1,40], and designed minimum distance d ≥ |I|+1 = 41 [i]
        3. linear OA(225, 61, F2, 9) (dual of [61, 36, 10]-code), using
  2. linear OA(2232, 574, F2, 48) (dual of [574, 342, 49]-code), using Gilbert–VarÅ¡amov bound and bm = 2232 > Vbs−1(k−1) = 2622 051055 330870 770868 838715 766284 722324 605702 891725 199965 782956 187032 [i]
  3. linear OA(21, 3, F2, 1) (dual of [3, 2, 2]-code), 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(2236, 578, F2, 51) (dual of [578, 342, 52]-code) [i]Adding a Parity Check Bit