Information on Result #1297673

Linear OA(2250, 558, F2, 56) (dual of [558, 308, 57]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(2242, 546, F2, 56) (dual of [546, 304, 57]-code), using
    • construction XX applied to C1 = C([507,50]), C2 = C([1,52]), C3 = C1 + C2 = C([1,50]), and C∩ = C1 ∩ C2 = C([507,52]) [i] based on
      1. 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 = {−4,−3,…,50}, and designed minimum distance d ≥ |I|+1 = 56 [i]
      2. linear OA(2216, 511, F2, 52) (dual of [511, 295, 53]-code), using the primitive narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [1,52], and designed minimum distance d ≥ |I|+1 = 53 [i]
      3. linear OA(2235, 511, F2, 57) (dual of [511, 276, 58]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−4,−3,…,52}, and designed minimum distance d ≥ |I|+1 = 58 [i]
      4. linear OA(2207, 511, F2, 50) (dual of [511, 304, 51]-code), using the primitive narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [1,50], and designed minimum distance d ≥ |I|+1 = 51 [i]
      5. linear OA(26, 25, F2, 3) (dual of [25, 19, 4]-code or 25-cap in PG(5,2)), using
      6. linear OA(21, 10, F2, 1) (dual of [10, 9, 2]-code), using
  2. linear OA(2242, 550, F2, 52) (dual of [550, 308, 53]-code), using Gilbert–VarÅ¡amov bound and bm = 2242 > Vbs−1(k−1) = 3 413558 892313 856782 849138 682635 222549 972234 907614 725012 369823 432411 828032 [i]
  3. linear OA(24, 8, F2, 3) (dual of [8, 4, 4]-code or 8-cap 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(2251, 559, F2, 57) (dual of [559, 308, 58]-code) [i]Adding a Parity Check Bit