Information on Result #686190
Linear OA(8114, 2097168, F8, 19) (dual of [2097168, 2097054, 20]-code), using construction X applied to C([0,9]) ⊂ C([0,8]) based on
- linear OA(8113, 2097153, F8, 19) (dual of [2097153, 2097040, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153 | 814−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(899, 2097153, F8, 17) (dual of [2097153, 2097054, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153 | 814−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (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(8115, 2097169, F8, 19) (dual of [2097169, 2097054, 20]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(8116, 2097170, F8, 19) (dual of [2097170, 2097054, 20]-code) | [i] | ||
| 3 | Linear OA(8116, 2097171, F8, 19) (dual of [2097171, 2097055, 20]-code) | [i] | Construction X with Varšamov Bound | |
| 4 | Linear OOA(8114, 1048584, F8, 2, 19) (dual of [(1048584, 2), 2097054, 20]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(8114, 699056, F8, 3, 19) (dual of [(699056, 3), 2097054, 20]-NRT-code) | [i] | ||
| 6 | Linear OOA(8114, 233018, F8, 19, 19) (dual of [(233018, 19), 4427228, 20]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |