Information on Result #1297348

Linear OA(2184, 276, F2, 54) (dual of [276, 92, 55]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(2179, 270, F2, 54) (dual of [270, 91, 55]-code), using
    • construction XX applied to C1 = C([253,50]), C2 = C([1,52]), C3 = C1 + C2 = C([1,50]), and C∩ = C1 ∩ C2 = C([253,52]) [i] based on
      1. linear OA(2173, 255, F2, 53) (dual of [255, 82, 54]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−2,−1,…,50}, and designed minimum distance d ≥ |I|+1 = 54 [i]
      2. linear OA(2168, 255, F2, 52) (dual of [255, 87, 53]-code), using the primitive narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [1,52], and designed minimum distance d ≥ |I|+1 = 53 [i]
      3. linear OA(2177, 255, F2, 55) (dual of [255, 78, 56]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−2,−1,…,52}, and designed minimum distance d ≥ |I|+1 = 56 [i]
      4. linear OA(2164, 255, F2, 50) (dual of [255, 91, 51]-code), using the primitive narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [1,50], and designed minimum distance d ≥ |I|+1 = 51 [i]
      5. linear OA(21, 10, F2, 1) (dual of [10, 9, 2]-code), using
      6. linear OA(21, 5, F2, 1) (dual of [5, 4, 2]-code), using
  2. linear OA(2179, 271, F2, 49) (dual of [271, 92, 50]-code), using Gilbert–VarÅ¡amov bound and bm = 2179 > Vbs−1(k−1) = 609183 930833 603167 280537 187271 712654 887333 962045 610736 [i]
  3. linear OA(24, 5, F2, 4) (dual of [5, 1, 5]-code or 5-arc in PG(3,2)), 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(2185, 277, F2, 55) (dual of [277, 92, 56]-code) [i]Adding a Parity Check Bit