Information on Result #663140
Linear OA(722, 21512, F7, 5) (dual of [21512, 21490, 6]-code), using generalized (u, u+v)-construction based on
- linear OA(70, 2801, F7, 0) (dual of [2801, 2801, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(70, s, F7, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(70, 2801, F7, 0) (dual of [2801, 2801, 1]-code) (see above)
- linear OA(71, 2801, F7, 1) (dual of [2801, 2800, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(71, s, F7, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- linear OA(71, 2801, F7, 1) (dual of [2801, 2800, 2]-code) (see above)
- linear OA(71, 2801, F7, 1) (dual of [2801, 2800, 2]-code) (see above)
- linear OA(75, 2801, F7, 2) (dual of [2801, 2796, 3]-code), using
- Hamming code H(5,7) [i]
- linear OA(714, 4706, F7, 5) (dual of [4706, 4692, 6]-code), using
- trace code [i] based on linear OA(497, 2353, F49, 5) (dual of [2353, 2346, 6]-code), using
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 OOA(722, 21512, F7, 2, 5) (dual of [(21512, 2), 43002, 6]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(722, 21512, F7, 3, 5) (dual of [(21512, 3), 64514, 6]-NRT-code) | [i] | ||
| 3 | Digital (17, 22, 21512)-net over F7 | [i] | ||
| 4 | Linear OOA(722, 10756, F7, 2, 5) (dual of [(10756, 2), 21490, 6]-NRT-code) | [i] | OOA Folding | |