Information on Result #1316044
Linear OA(8128, 505, F81, 15) (dual of [505, 477, 16]-code), using 90 step Varšamov–Edel lengthening with (ri) = (1, 89 times 0) based on linear OA(8127, 414, F81, 15) (dual of [414, 387, 16]-code), using
- construction XX applied to C1 = C([34,47]), C2 = C([33,46]), C3 = C1 + C2 = C([34,46]), and C∩ = C1 ∩ C2 = C([33,47]) [i] based on
- 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(8125, 410, F81, 14) (dual of [410, 385, 15]-code), using the BCH-code C(I) with length 410 | 812−1, defining interval I = {33,34,…,46}, and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(8127, 410, F81, 15) (dual of [410, 383, 16]-code), using the BCH-code C(I) with length 410 | 812−1, defining interval I = {33,34,…,47}, and designed minimum distance d ≥ |I|+1 = 16 [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(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: 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 OOA(8128, 505, F81, 2, 15) (dual of [(505, 2), 982, 16]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(8128, 505, F81, 3, 15) (dual of [(505, 3), 1487, 16]-NRT-code) | [i] | ||
| 3 | Linear OOA(8128, 505, F81, 4, 15) (dual of [(505, 4), 1992, 16]-NRT-code) | [i] | ||
| 4 | Digital (13, 28, 505)-net over F81 | [i] | ||