Information on Result #699661
Linear OA(12820, 2097160, F128, 7) (dual of [2097160, 2097140, 8]-code), using construction X applied to C([0,3]) ⊂ C([0,2]) 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
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(12820, 2086556, F128, 2, 7) (dual of [(2086556, 2), 4173092, 8]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(12820, 2086556, F128, 3, 7) (dual of [(2086556, 3), 6259648, 8]-NRT-code) | [i] | ||
| 3 | Linear OOA(12820, 2086556, F128, 4, 7) (dual of [(2086556, 4), 8346204, 8]-NRT-code) | [i] | ||
| 4 | Digital (13, 20, 2086556)-net over F128 | [i] | ||
| 5 | Linear OOA(12820, 1048580, F128, 2, 7) (dual of [(1048580, 2), 2097140, 8]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(12820, 699053, F128, 3, 7) (dual of [(699053, 3), 2097139, 8]-NRT-code) | [i] | ||
| 7 | Linear OOA(12820, 699053, F128, 4, 7) (dual of [(699053, 4), 2796192, 8]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |
| 8 | Linear OOA(12820, 699053, F128, 7, 7) (dual of [(699053, 7), 4893351, 8]-NRT-code) | [i] | ||