Information on Result #1019197
Linear OOA(12853, 2828714, F128, 3, 11) (dual of [(2828714, 3), 8486089, 12]-NRT-code), using (u, u+v)-construction based on
- linear OOA(12812, 32513, F128, 3, 5) (dual of [(32513, 3), 97527, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(12812, 65027, F128, 5) (dual of [65027, 65015, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(12812, 65028, F128, 5) (dual of [65028, 65016, 6]-code), using
- generalized (u, u+v)-construction [i] based on
- linear OA(1281, 16257, F128, 1) (dual of [16257, 16256, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(1281, s, F128, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- linear OA(1281, 16257, F128, 1) (dual of [16257, 16256, 2]-code) (see above)
- linear OA(1283, 16257, F128, 2) (dual of [16257, 16254, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(1283, 16513, F128, 2) (dual of [16513, 16510, 3]-code), using
- Hamming code H(3,128) [i]
- discarding factors / shortening the dual code based on linear OA(1283, 16513, F128, 2) (dual of [16513, 16510, 3]-code), using
- linear OA(1287, 16257, F128, 5) (dual of [16257, 16250, 6]-code), using
- linear OA(1281, 16257, F128, 1) (dual of [16257, 16256, 2]-code), using
- generalized (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OA(12812, 65028, F128, 5) (dual of [65028, 65016, 6]-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(12812, 65027, F128, 5) (dual of [65027, 65015, 6]-code), using
- linear OOA(12841, 2796201, F128, 3, 11) (dual of [(2796201, 3), 8388562, 12]-NRT-code), using
- OOA 3-folding [i] based on linear OA(12841, large, F128, 11) (dual of [large, large−41, 12]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 15790321 | 1288−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- OOA 3-folding [i] based on linear OA(12841, large, F128, 11) (dual of [large, large−41, 12]-code), using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m 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(12870, 5657428, F128, 3, 11) (dual of [(5657428, 3), 16972214, 12]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |