Information on Result #1297689

Linear OA(2246, 569, F2, 54) (dual of [569, 323, 55]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(2243, 565, F2, 54) (dual of [565, 322, 55]-code), using
    • construction XX applied to C1 = C([461,510]), C2 = C([467,4]), C3 = C1 + C2 = C([467,510]), and C∩ = C1 ∩ C2 = C([461,4]) [i] based on
      1. linear OA(2207, 511, F2, 50) (dual of [511, 304, 51]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−50,−49,…,−1}, and designed minimum distance d ≥ |I|+1 = 51 [i]
      2. linear OA(2208, 511, F2, 49) (dual of [511, 303, 50]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−44,−43,…,4}, and designed minimum distance d ≥ |I|+1 = 50 [i]
      3. linear OA(2226, 511, F2, 55) (dual of [511, 285, 56]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−50,−49,…,4}, and designed minimum distance d ≥ |I|+1 = 56 [i]
      4. linear OA(2189, 511, F2, 44) (dual of [511, 322, 45]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−44,−43,…,−1}, and designed minimum distance d ≥ |I|+1 = 45 [i]
      5. linear OA(211, 29, F2, 5) (dual of [29, 18, 6]-code), using
      6. linear OA(26, 25, F2, 3) (dual of [25, 19, 4]-code or 25-cap in PG(5,2)), using
  2. linear OA(2243, 566, F2, 51) (dual of [566, 323, 52]-code), using Gilbert–VarÅ¡amov bound and bm = 2243 > Vbs−1(k−1) = 1 559984 984189 704211 507623 460383 106708 467115 547968 868307 200627 757975 698920 [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(2247, 570, F2, 55) (dual of [570, 323, 56]-code) [i]Adding a Parity Check Bit