Information on Result #701799

Linear OA(2113, 300, F2, 26) (dual of [300, 187, 27]-code), using construction XX applied to C1 = C([251,18]), C2 = C([1,22]), C3 = C1 + C2 = C([1,18]), and C∩ = C1 ∩ C2 = C([251,22]) based on
  1. linear OA(285, 255, F2, 23) (dual of [255, 170, 24]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−4,−3,…,18}, and designed minimum distance d ≥ |I|+1 = 24 [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(268, 255, F2, 18) (dual of [255, 187, 19]-code), using the primitive narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [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(26, 22, F2, 3) (dual of [22, 16, 4]-code or 22-cap in PG(5,2)), 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(2114, 301, F2, 27) (dual of [301, 187, 28]-code) [i]Adding a Parity Check Bit
2Linear OA(2116, 304, F2, 26) (dual of [304, 188, 27]-code) [i]Construction X with VarÅ¡amov Bound
3Linear OOA(2113, 150, F2, 2, 26) (dual of [(150, 2), 187, 27]-NRT-code) [i]OOA Folding
4Linear OOA(2113, 100, F2, 3, 26) (dual of [(100, 3), 187, 27]-NRT-code) [i]
5Linear OOA(2113, 75, F2, 4, 26) (dual of [(75, 4), 187, 27]-NRT-code) [i]