Information on Result #730413
Linear OA(8143, 824, F81, 23) (dual of [824, 781, 24]-code), using construction XX applied to C1 = C([31,52]), C2 = C([30,51]), C3 = C1 + C2 = C([31,51]), and C∩ = C1 ∩ C2 = C([30,52]) based on
- linear OA(8141, 820, F81, 22) (dual of [820, 779, 23]-code), using the BCH-code C(I) with length 820 | 812−1, defining interval I = {31,32,…,52}, and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(8141, 820, F81, 22) (dual of [820, 779, 23]-code), using the BCH-code C(I) with length 820 | 812−1, defining interval I = {30,31,…,51}, and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(8143, 820, F81, 23) (dual of [820, 777, 24]-code), using the BCH-code C(I) with length 820 | 812−1, defining interval I = {30,31,…,52}, and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(8139, 820, F81, 21) (dual of [820, 781, 22]-code), using the BCH-code C(I) with length 820 | 812−1, defining interval I = {31,32,…,51}, and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(810, 2, F81, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(810, s, F81, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- 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:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | OA(2758, 824, S27, 23) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OOA(8143, 412, F81, 2, 23) (dual of [(412, 2), 781, 24]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(8143, 206, F81, 4, 23) (dual of [(206, 4), 781, 24]-NRT-code) | [i] | ||