Information on Result #698915
Linear OA(6486, 4119, F64, 40) (dual of [4119, 4033, 41]-code), using construction X applied to Ce(39) ⊂ Ce(31) based on
- linear OA(6479, 4096, F64, 40) (dual of [4096, 4017, 41]-code), using an extension Ce(39) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,39], and designed minimum distance d ≥ |I|+1 = 40 [i]
- linear OA(6463, 4096, F64, 32) (dual of [4096, 4033, 33]-code), using an extension Ce(31) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,31], and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(647, 23, F64, 7) (dual of [23, 16, 8]-code or 23-arc in PG(6,64)), using
- discarding factors / shortening the dual code based on linear OA(647, 64, F64, 7) (dual of [64, 57, 8]-code or 64-arc in PG(6,64)), using
- Reed–Solomon code RS(57,64) [i]
- discarding factors / shortening the dual code based on linear OA(647, 64, F64, 7) (dual of [64, 57, 8]-code or 64-arc in PG(6,64)), 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 OA(8172, 8238, F8, 40) (dual of [8238, 8066, 41]-code) | [i] | Trace Code | |
| 2 | OA(32104, 4119, S32, 40) | [i] | Discarding Parts of the Base for OAs | |
| 3 | Linear OOA(6486, 2598, F64, 2, 40) (dual of [(2598, 2), 5110, 41]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(6486, 2598, F64, 3, 40) (dual of [(2598, 3), 7708, 41]-NRT-code) | [i] | ||
| 5 | Digital (46, 86, 2598)-net over F64 | [i] | ||
| 6 | Linear OOA(6486, 2059, F64, 2, 40) (dual of [(2059, 2), 4032, 41]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(6486, 1373, F64, 3, 40) (dual of [(1373, 3), 4033, 41]-NRT-code) | [i] | ||