Information on Result #730437
Linear OA(8181, 824, F81, 43) (dual of [824, 743, 44]-code), using construction XX applied to C1 = C([21,62]), C2 = C([20,61]), C3 = C1 + C2 = C([21,61]), and C∩ = C1 ∩ C2 = C([20,62]) based on
- linear OA(8179, 820, F81, 42) (dual of [820, 741, 43]-code), using the BCH-code C(I) with length 820 | 812−1, defining interval I = {21,22,…,62}, and designed minimum distance d ≥ |I|+1 = 43 [i]
- linear OA(8179, 820, F81, 42) (dual of [820, 741, 43]-code), using the BCH-code C(I) with length 820 | 812−1, defining interval I = {20,21,…,61}, and designed minimum distance d ≥ |I|+1 = 43 [i]
- linear OA(8181, 820, F81, 43) (dual of [820, 739, 44]-code), using the BCH-code C(I) with length 820 | 812−1, defining interval I = {20,21,…,62}, and designed minimum distance d ≥ |I|+1 = 44 [i]
- linear OA(8177, 820, F81, 41) (dual of [820, 743, 42]-code), using the BCH-code C(I) with length 820 | 812−1, defining interval I = {21,22,…,61}, and designed minimum distance d ≥ |I|+1 = 42 [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(27108, 824, S27, 43) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OOA(8181, 412, F81, 2, 43) (dual of [(412, 2), 743, 44]-NRT-code) | [i] | OOA Folding | |