Information on Result #698510
Linear OA(6431, 262159, F64, 10) (dual of [262159, 262128, 11]-code), using construction X applied to Ce(9) ⊂ Ce(5) based on
- linear OA(6428, 262144, F64, 10) (dual of [262144, 262116, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(6416, 262144, F64, 6) (dual of [262144, 262128, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [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 | Linear OOA(6431, 262159, F64, 2, 10) (dual of [(262159, 2), 524287, 11]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(6431, 262159, F64, 3, 10) (dual of [(262159, 3), 786446, 11]-NRT-code) | [i] | ||
| 3 | Digital (21, 31, 262159)-net over F64 | [i] | ||
| 4 | Linear OOA(6431, 131079, F64, 2, 10) (dual of [(131079, 2), 262127, 11]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(6431, 87386, F64, 3, 10) (dual of [(87386, 3), 262127, 11]-NRT-code) | [i] | ||