Information on Result #1297633

Linear OA(2251, 299, F2, 92) (dual of [299, 48, 93]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(2237, 284, F2, 92) (dual of [284, 47, 93]-code), using
    • construction XX applied to C1 = C([165,254]), C2 = C([171,4]), C3 = C1 + C2 = C([171,254]), and C∩ = C1 ∩ C2 = C([165,4]) [i] based on
      1. linear OA(2218, 255, F2, 90) (dual of [255, 37, 91]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−90,−89,…,−1}, and designed minimum distance d ≥ |I|+1 = 91 [i]
      2. linear OA(2217, 255, F2, 89) (dual of [255, 38, 90]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−84,−83,…,4}, and designed minimum distance d ≥ |I|+1 = 90 [i]
      3. linear OA(2227, 255, F2, 95) (dual of [255, 28, 96]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−90,−89,…,4}, and designed minimum distance d ≥ |I|+1 = 96 [i]
      4. linear OA(2208, 255, F2, 84) (dual of [255, 47, 85]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−84,−83,…,−1}, and designed minimum distance d ≥ |I|+1 = 85 [i]
      5. linear OA(25, 15, F2, 3) (dual of [15, 10, 4]-code or 15-cap in PG(4,2)), using
      6. linear OA(25, 14, F2, 3) (dual of [14, 9, 4]-code or 14-cap in PG(4,2)), using
  2. linear OA(2237, 285, F2, 78) (dual of [285, 48, 79]-code), using Gilbert–VarÅ¡amov bound and bm = 2237 > Vbs−1(k−1) = 100189 079425 600164 500660 620157 034605 945785 490950 864232 014891 547063 214704 [i]
  3. linear OA(213, 14, F2, 13) (dual of [14, 1, 14]-code or 14-arc in PG(12,2)), 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(2252, 300, F2, 93) (dual of [300, 48, 94]-code) [i]Adding a Parity Check Bit