Information on Result #702659

Linear OA(2237, 532, F2, 56) (dual of [532, 295, 57]-code), using construction XX applied to C1 = C([509,52]), C2 = C([1,54]), C3 = C1 + C2 = C([1,52]), and C∩ = C1 ∩ C2 = C([509,54]) 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 = {−2,−1,…,52}, and designed minimum distance d ≥ |I|+1 = 56 [i]
  2. linear OA(2225, 511, F2, 54) (dual of [511, 286, 55]-code), using the primitive narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [1,54], and designed minimum distance d ≥ |I|+1 = 55 [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 = {−2,−1,…,54}, and designed minimum distance d ≥ |I|+1 = 58 [i]
  4. 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]
  5. linear OA(21, 11, F2, 1) (dual of [11, 10, 2]-code), 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(2238, 533, F2, 57) (dual of [533, 295, 58]-code) [i]Adding a Parity Check Bit
2Linear OOA(2237, 266, F2, 2, 56) (dual of [(266, 2), 295, 57]-NRT-code) [i]OOA Folding
3Linear OOA(2237, 177, F2, 3, 56) (dual of [(177, 3), 294, 57]-NRT-code) [i]