Information on Result #730235
Linear OA(8125, 414, F81, 14) (dual of [414, 389, 15]-code), using construction XX applied to C1 = C([35,47]), C2 = C([34,46]), C3 = C1 + C2 = C([35,46]), and C∩ = C1 ∩ C2 = C([34,47]) based on
- linear OA(8123, 410, F81, 13) (dual of [410, 387, 14]-code), using the BCH-code C(I) with length 410 | 812−1, defining interval I = {35,36,…,47}, and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(8123, 410, F81, 13) (dual of [410, 387, 14]-code), using the BCH-code C(I) with length 410 | 812−1, defining interval I = {34,35,…,46}, and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(8125, 410, F81, 14) (dual of [410, 385, 15]-code), using the BCH-code C(I) with length 410 | 812−1, defining interval I = {34,35,…,47}, and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(8121, 410, F81, 12) (dual of [410, 389, 13]-code), using the BCH-code C(I) with length 410 | 812−1, defining interval I = {35,36,…,46}, and designed minimum distance d ≥ |I|+1 = 13 [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 | Linear OA(8182, 6977, F81, 29) (dual of [6977, 6895, 30]-code) | [i] | (u, u+v)-Construction | |
| 2 | Linear OA(8180, 6977, F81, 28) (dual of [6977, 6897, 29]-code) | [i] | ||
| 3 | Linear OOA(8125, 414, F81, 2, 14) (dual of [(414, 2), 803, 15]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(8125, 414, F81, 3, 14) (dual of [(414, 3), 1217, 15]-NRT-code) | [i] | ||
| 5 | Linear OOA(8125, 414, F81, 4, 14) (dual of [(414, 4), 1631, 15]-NRT-code) | [i] | ||
| 6 | Digital (11, 25, 414)-net over F81 | [i] | ||
| 7 | Linear OA(8126, 477, F81, 14) (dual of [477, 451, 15]-code) | [i] | Varšamov–Edel Lengthening | |
| 8 | Linear OOA(8125, 207, F81, 2, 14) (dual of [(207, 2), 389, 15]-NRT-code) | [i] | OOA Folding | |
| 9 | Linear OOA(8125, 138, F81, 3, 14) (dual of [(138, 3), 389, 15]-NRT-code) | [i] | ||