Information on Result #731391
Linear OA(976, 13144, F9, 18) (dual of [13144, 13068, 19]-code), using trace code based on linear OA(8138, 6572, F81, 18) (dual of [6572, 6534, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(13) [i] based on
- linear OA(8135, 6561, F81, 18) (dual of [6561, 6526, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(8127, 6561, F81, 14) (dual of [6561, 6534, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [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(977, 13145, F9, 18) (dual of [13145, 13068, 19]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(976, 6572, F9, 2, 18) (dual of [(6572, 2), 13068, 19]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(976, 4381, F9, 3, 18) (dual of [(4381, 3), 13067, 19]-NRT-code) | [i] | ||
| 4 | Linear OOA(976, 1460, F9, 18, 18) (dual of [(1460, 18), 26204, 19]-NRT-code) | [i] | OA Folding and Stacking | |