Information on Result #1464413
Linear OOA(12820, 2086556, F128, 2, 7) (dual of [(2086556, 2), 4173092, 8]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(12820, 2086556, F128, 7) (dual of [2086556, 2086536, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(12820, 2097160, F128, 7) (dual of [2097160, 2097140, 8]-code), using
- construction X applied to C([0,3]) ⊂ C([0,2]) [i] based on
- linear OA(12819, 2097153, F128, 7) (dual of [2097153, 2097134, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153 | 1286−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- linear OA(12813, 2097153, F128, 5) (dual of [2097153, 2097140, 6]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153 | 1286−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (BCH-bound) [i]
- linear OA(1281, 7, F128, 1) (dual of [7, 6, 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
- construction X applied to C([0,3]) ⊂ C([0,2]) [i] based on
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 | OOA(6424, 2086556, S64, 2, 7) | [i] | Discarding Parts of the Base for OOAs | |
| 2 | Linear OOA(12820, 1043278, F128, 3, 7) (dual of [(1043278, 3), 3129814, 8]-NRT-code) | [i] | OOA Folding | |