Information on Result #701822

Linear OA(2121, 300, F2, 28) (dual of [300, 179, 29]-code), using construction XX applied to C1 = C([251,20]), C2 = C([1,24]), C3 = C1 + C2 = C([1,20]), and C∩ = C1 ∩ C2 = C([251,24]) 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(292, 255, F2, 24) (dual of [255, 163, 25]-code), using the primitive narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
  3. linear OA(2109, 255, F2, 29) (dual of [255, 146, 30]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−4,−3,…,24}, and designed minimum distance d ≥ |I|+1 = 30 [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(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(2122, 301, F2, 29) (dual of [301, 179, 30]-code) [i]Adding a Parity Check Bit
2Linear OA(2123, 303, F2, 28) (dual of [303, 180, 29]-code) [i]Construction X with VarÅ¡amov Bound
3Linear OA(2124, 305, F2, 28) (dual of [305, 181, 29]-code) [i]
4Linear OOA(2121, 150, F2, 2, 28) (dual of [(150, 2), 179, 29]-NRT-code) [i]OOA Folding
5Linear OOA(2121, 100, F2, 3, 28) (dual of [(100, 3), 179, 29]-NRT-code) [i]