Information on Result #702666

Linear OA(2251, 545, F2, 59) (dual of [545, 294, 60]-code), using construction XX applied to C1 = C([507,52]), C2 = C([0,54]), C3 = C1 + C2 = C([0,52]), and C∩ = C1 ∩ C2 = C([507,54]) based on
  1. 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]
  2. linear OA(2226, 511, F2, 55) (dual of [511, 285, 56]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [0,54], and designed minimum distance d ≥ |I|+1 = 56 [i]
  3. linear OA(2244, 511, F2, 59) (dual of [511, 267, 60]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−4,−3,…,54}, and designed minimum distance d ≥ |I|+1 = 60 [i]
  4. linear OA(2217, 511, F2, 53) (dual of [511, 294, 54]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [0,52], and designed minimum distance d ≥ |I|+1 = 54 [i]
  5. linear OA(26, 24, F2, 3) (dual of [24, 18, 4]-code or 24-cap in PG(5,2)), using
  6. linear OA(21, 10, F2, 1) (dual of [10, 9, 2]-code), using

Mode: Constructive and 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(2250, 544, F2, 58) (dual of [544, 294, 59]-code) [i]Truncation
2Linear OOA(2251, 272, F2, 2, 59) (dual of [(272, 2), 293, 60]-NRT-code) [i]OOA Folding
3Linear OOA(2251, 181, F2, 3, 59) (dual of [(181, 3), 292, 60]-NRT-code) [i]
4Linear OOA(2251, 109, F2, 5, 59) (dual of [(109, 5), 294, 60]-NRT-code) [i]