Information on Result #1297239

Linear OA(2116, 304, F2, 26) (dual of [304, 188, 27]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(2113, 300, F2, 26) (dual of [300, 187, 27]-code), using
    • construction XX applied to C1 = C([251,18]), C2 = C([1,22]), C3 = C1 + C2 = C([1,18]), and C∩ = C1 ∩ C2 = C([251,22]) [i] based on
      1. linear OA(285, 255, F2, 23) (dual of [255, 170, 24]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−4,−3,…,18}, and designed minimum distance d ≥ |I|+1 = 24 [i]
      2. linear OA(284, 255, F2, 22) (dual of [255, 171, 23]-code), using the primitive narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
      3. linear OA(2101, 255, F2, 27) (dual of [255, 154, 28]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−4,−3,…,22}, and designed minimum distance d ≥ |I|+1 = 28 [i]
      4. linear OA(268, 255, F2, 18) (dual of [255, 187, 19]-code), using the primitive narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
      5. linear OA(26, 23, F2, 3) (dual of [23, 17, 4]-code or 23-cap in PG(5,2)), using
      6. linear OA(26, 22, F2, 3) (dual of [22, 16, 4]-code or 22-cap in PG(5,2)), using
  2. linear OA(2113, 301, F2, 23) (dual of [301, 188, 24]-code), using Gilbert–VarÅ¡amov bound and bm = 2113 > Vbs−1(k−1) = 1376 333619 401094 948219 496047 900836 [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(2117, 305, F2, 27) (dual of [305, 188, 28]-code) [i]Adding a Parity Check Bit