Information on Result #730422

Linear OA(8151, 824, F81, 27) (dual of [824, 773, 28]-code), using construction XX applied to C1 = C([27,52]), C2 = C([26,51]), C3 = C1 + C2 = C([27,51]), and C∩ = C1 ∩ C2 = C([26,52]) based on
  1. linear OA(8149, 820, F81, 26) (dual of [820, 771, 27]-code), using the BCH-code C(I) with length 820 | 812−1, defining interval I = {27,28,…,52}, and designed minimum distance d ≥ |I|+1 = 27 [i]
  2. linear OA(8149, 820, F81, 26) (dual of [820, 771, 27]-code), using the BCH-code C(I) with length 820 | 812−1, defining interval I = {26,27,…,51}, and designed minimum distance d ≥ |I|+1 = 27 [i]
  3. linear OA(8151, 820, F81, 27) (dual of [820, 769, 28]-code), using the BCH-code C(I) with length 820 | 812−1, defining interval I = {26,27,…,52}, and designed minimum distance d ≥ |I|+1 = 28 [i]
  4. linear OA(8147, 820, F81, 25) (dual of [820, 773, 26]-code), using the BCH-code C(I) with length 820 | 812−1, defining interval I = {27,28,…,51}, and designed minimum distance d ≥ |I|+1 = 26 [i]
  5. linear OA(810, 2, F81, 0) (dual of [2, 2, 1]-code), using
  6. linear OA(810, 2, F81, 0) (dual of [2, 2, 1]-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
1OA(2768, 824, S27, 27) [i]Discarding Parts of the Base for OAs
2Linear OOA(8151, 824, F81, 2, 27) (dual of [(824, 2), 1597, 28]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
3Linear OOA(8151, 824, F81, 3, 27) (dual of [(824, 3), 2421, 28]-NRT-code) [i]
4Linear OOA(8151, 824, F81, 4, 27) (dual of [(824, 4), 3245, 28]-NRT-code) [i]
5Digital (24, 51, 824)-net over F81 [i]
6Linear OOA(8151, 412, F81, 2, 27) (dual of [(412, 2), 773, 28]-NRT-code) [i]OOA Folding
7Linear OOA(8151, 206, F81, 4, 27) (dual of [(206, 4), 773, 28]-NRT-code) [i]