Information on Result #731384
Linear OA(972, 13146, F9, 17) (dual of [13146, 13074, 18]-code), using trace code based on linear OA(8136, 6573, F81, 17) (dual of [6573, 6537, 18]-code), using
- construction X applied to C([0,8]) ⊂ C([0,6]) [i] based on
- linear OA(8133, 6562, F81, 17) (dual of [6562, 6529, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 814−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(8125, 6562, F81, 13) (dual of [6562, 6537, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 814−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(813, 11, F81, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,81) or 11-cap in PG(2,81)), using
- discarding factors / shortening the dual code based on linear OA(813, 81, F81, 3) (dual of [81, 78, 4]-code or 81-arc in PG(2,81) or 81-cap in PG(2,81)), using
- Reed–Solomon code RS(78,81) [i]
- discarding factors / shortening the dual code based on linear OA(813, 81, F81, 3) (dual of [81, 78, 4]-code or 81-arc in PG(2,81) or 81-cap in PG(2,81)), 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(973, 13147, F9, 17) (dual of [13147, 13074, 18]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(972, 6573, F9, 2, 17) (dual of [(6573, 2), 13074, 18]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(972, 4382, F9, 3, 17) (dual of [(4382, 3), 13074, 18]-NRT-code) | [i] | ||
| 4 | Linear OOA(972, 1643, F9, 17, 17) (dual of [(1643, 17), 27859, 18]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |