Information on Result #698506
Linear OA(6455, 262159, F64, 18) (dual of [262159, 262104, 19]-code), using construction X applied to Ce(17) ⊂ Ce(13) based on
- linear OA(6452, 262144, F64, 18) (dual of [262144, 262092, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(6440, 262144, F64, 14) (dual of [262144, 262104, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(643, 15, F64, 3) (dual of [15, 12, 4]-code or 15-arc in PG(2,64) or 15-cap in PG(2,64)), using
- discarding factors / shortening the dual code based on linear OA(643, 64, F64, 3) (dual of [64, 61, 4]-code or 64-arc in PG(2,64) or 64-cap in PG(2,64)), using
- Reed–Solomon code RS(61,64) [i]
- discarding factors / shortening the dual code based on linear OA(643, 64, F64, 3) (dual of [64, 61, 4]-code or 64-arc in PG(2,64) or 64-cap in PG(2,64)), 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 | OA(3266, 262159, S32, 18) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OOA(6455, 134596, F64, 2, 18) (dual of [(134596, 2), 269137, 19]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(6455, 134596, F64, 3, 18) (dual of [(134596, 3), 403733, 19]-NRT-code) | [i] | ||
| 4 | Digital (37, 55, 134596)-net over F64 | [i] | ||
| 5 | Linear OOA(6455, 131079, F64, 2, 18) (dual of [(131079, 2), 262103, 19]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(6455, 87386, F64, 3, 18) (dual of [(87386, 3), 262103, 19]-NRT-code) | [i] | ||