Information on Result #663199
Linear OA(711, 129, F7, 5) (dual of [129, 118, 6]-code), using (u, u−v, u+v+w)-construction based on
- linear OA(71, 43, F7, 1) (dual of [43, 42, 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(73, 43, F7, 2) (dual of [43, 40, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(73, 48, F7, 2) (dual of [48, 45, 3]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 3 [i]
- discarding factors / shortening the dual code based on linear OA(73, 48, F7, 2) (dual of [48, 45, 3]-code), using
- linear OA(77, 43, F7, 5) (dual of [43, 36, 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(711, 129, F7, 2, 5) (dual of [(129, 2), 247, 6]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(711, 129, F7, 3, 5) (dual of [(129, 3), 376, 6]-NRT-code) | [i] | ||
| 3 | Digital (6, 11, 129)-net over F7 | [i] | ||
| 4 | Linear OOA(711, 64, F7, 2, 5) (dual of [(64, 2), 117, 6]-NRT-code) | [i] | OOA Folding | |