Information on Result #731532
Linear OA(9146, 1062912, F9, 24) (dual of [1062912, 1062766, 25]-code), using trace code based on linear OA(8173, 531456, F81, 24) (dual of [531456, 531383, 25]-code), using
- construction X applied to Ce(23) ⊂ Ce(19) [i] based on
- linear OA(8170, 531441, F81, 24) (dual of [531441, 531371, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(8158, 531441, F81, 20) (dual of [531441, 531383, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(813, 15, F81, 3) (dual of [15, 12, 4]-code or 15-arc in PG(2,81) or 15-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(9147, 1062913, F9, 24) (dual of [1062913, 1062766, 25]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(9146, 531456, F9, 2, 24) (dual of [(531456, 2), 1062766, 25]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(9146, 354304, F9, 3, 24) (dual of [(354304, 3), 1062766, 25]-NRT-code) | [i] | ||
| 4 | Linear OOA(9146, 88576, F9, 24, 24) (dual of [(88576, 24), 2125678, 25]-NRT-code) | [i] | OA Folding and Stacking | |