Information on Result #701805

Linear OA(2108, 287, F2, 26) (dual of [287, 179, 27]-code), using construction XX applied to C1 = C([251,20]), C2 = C([1,22]), C3 = C1 + C2 = C([1,20]), and C∩ = C1 ∩ C2 = C([251,22]) based on
  1. linear OA(293, 255, F2, 25) (dual of [255, 162, 26]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−4,−3,…,20}, and designed minimum distance d ≥ |I|+1 = 26 [i]
  2. linear OA(284, 255, F2, 22) (dual of [255, 171, 23]-code), using the primitive narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
  3. linear OA(2101, 255, F2, 27) (dual of [255, 154, 28]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−4,−3,…,22}, and designed minimum distance d ≥ |I|+1 = 28 [i]
  4. linear OA(276, 255, F2, 20) (dual of [255, 179, 21]-code), using the primitive narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
  5. linear OA(26, 23, F2, 3) (dual of [23, 17, 4]-code or 23-cap in PG(5,2)), using
  6. linear OA(21, 9, F2, 1) (dual of [9, 8, 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(2110, 289, F2, 26) (dual of [289, 179, 27]-code) [i]Code Embedding in Larger Space
2Linear OA(2109, 288, F2, 27) (dual of [288, 179, 28]-code) [i]Adding a Parity Check Bit
3Linear OOA(2108, 143, F2, 2, 26) (dual of [(143, 2), 178, 27]-NRT-code) [i]OOA Folding