Information on Result #1297249

Linear OA(2123, 303, F2, 28) (dual of [303, 180, 29]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(2121, 300, F2, 28) (dual of [300, 179, 29]-code), using
    • construction XX applied to C1 = C([251,20]), C2 = C([1,24]), C3 = C1 + C2 = C([1,20]), and C∩ = C1 ∩ C2 = C([251,24]) [i] based on
      1. linear OA(293, 255, F2, 25) (dual of [255, 162, 26]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−4,−3,…,20}, and designed minimum distance d ≥ |I|+1 = 26 [i]
      2. linear OA(292, 255, F2, 24) (dual of [255, 163, 25]-code), using the primitive narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
      3. linear OA(2109, 255, F2, 29) (dual of [255, 146, 30]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−4,−3,…,24}, and designed minimum distance d ≥ |I|+1 = 30 [i]
      4. linear OA(276, 255, F2, 20) (dual of [255, 179, 21]-code), using the primitive narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [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(2121, 301, F2, 26) (dual of [301, 180, 27]-code), using Gilbert–VarÅ¡amov bound and bm = 2121 > Vbs−1(k−1) = 2 146897 010422 463915 699968 006884 692498 [i]
  3. linear OA(21, 2, F2, 1) (dual of [2, 1, 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(2124, 304, F2, 29) (dual of [304, 180, 30]-code) [i]Adding a Parity Check Bit