Information on Result #686188
Linear OA(8142, 2097168, F8, 23) (dual of [2097168, 2097026, 24]-code), using construction X applied to C([0,11]) ⊂ C([0,10]) based on
- linear OA(8141, 2097153, F8, 23) (dual of [2097153, 2097012, 24]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153 | 814−1, defining interval I = [0,11], and minimum distance d ≥ |{−11,−10,…,11}|+1 = 24 (BCH-bound) [i]
- linear OA(8127, 2097153, F8, 21) (dual of [2097153, 2097026, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153 | 814−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(81, 15, F8, 1) (dual of [15, 14, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(81, s, F8, 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 OA(8143, 2097169, F8, 23) (dual of [2097169, 2097026, 24]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(8142, 1435473, F8, 2, 23) (dual of [(1435473, 2), 2870804, 24]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(8142, 1435473, F8, 3, 23) (dual of [(1435473, 3), 4306277, 24]-NRT-code) | [i] | ||
| 4 | Digital (119, 142, 1435473)-net over F8 | [i] | ||
| 5 | Linear OOA(8142, 1048584, F8, 2, 23) (dual of [(1048584, 2), 2097026, 24]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(8142, 699056, F8, 3, 23) (dual of [(699056, 3), 2097026, 24]-NRT-code) | [i] | ||
| 7 | Linear OOA(8142, 190651, F8, 23, 23) (dual of [(190651, 23), 4384831, 24]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |