Information on Result #702642

Linear OA(2228, 531, F2, 55) (dual of [531, 303, 56]-code), using construction XX applied to C1 = C([509,50]), C2 = C([0,52]), C3 = C1 + C2 = C([0,50]), and C∩ = C1 ∩ C2 = C([509,52]) based on
  1. linear OA(2217, 511, F2, 53) (dual of [511, 294, 54]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−2,−1,…,50}, and designed minimum distance d ≥ |I|+1 = 54 [i]
  2. 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]
  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 = {−2,−1,…,52}, and designed minimum distance d ≥ |I|+1 = 56 [i]
  4. linear OA(2208, 511, F2, 51) (dual of [511, 303, 52]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [0,50], and designed minimum distance d ≥ |I|+1 = 52 [i]
  5. linear OA(21, 10, F2, 1) (dual of [10, 9, 2]-code), using
  6. linear OA(21, 10, F2, 1) (dual of [10, 9, 2]-code) (see above)

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(2227, 530, F2, 54) (dual of [530, 303, 55]-code) [i]Truncation
2Linear OOA(2228, 265, F2, 2, 55) (dual of [(265, 2), 302, 56]-NRT-code) [i]OOA Folding
3Linear OOA(2228, 177, F2, 3, 55) (dual of [(177, 3), 303, 56]-NRT-code) [i]
4Linear OOA(2228, 132, F2, 4, 55) (dual of [(132, 4), 300, 56]-NRT-code) [i]
5Linear OOA(2228, 106, F2, 5, 55) (dual of [(106, 5), 302, 56]-NRT-code) [i]