Information on Result #731408
Linear OA(988, 1062898, F9, 15) (dual of [1062898, 1062810, 16]-code), using trace code based on linear OA(8144, 531449, F81, 15) (dual of [531449, 531405, 16]-code), using
- construction X applied to C([0,7]) ⊂ C([0,6]) [i] based on
- linear OA(8143, 531442, F81, 15) (dual of [531442, 531399, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442 | 816−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- linear OA(8137, 531442, F81, 13) (dual of [531442, 531405, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442 | 816−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(811, 7, F81, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(811, s, F81, 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(989, 1062899, F9, 15) (dual of [1062899, 1062810, 16]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(988, 1062898, F9, 2, 15) (dual of [(1062898, 2), 2125708, 16]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(988, 1062898, F9, 3, 15) (dual of [(1062898, 3), 3188606, 16]-NRT-code) | [i] | ||
| 4 | Digital (73, 88, 1062898)-net over F9 | [i] | ||
| 5 | Linear OA(989, 1062900, F9, 15) (dual of [1062900, 1062811, 16]-code) | [i] | Construction X with Varšamov Bound | |
| 6 | Linear OOA(988, 531449, F9, 2, 15) (dual of [(531449, 2), 1062810, 16]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(988, 354299, F9, 3, 15) (dual of [(354299, 3), 1062809, 16]-NRT-code) | [i] | ||
| 8 | Linear OOA(988, 151842, F9, 15, 15) (dual of [(151842, 15), 2277542, 16]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |