Information on Result #698859
Linear OA(6439, 4110, F64, 18) (dual of [4110, 4071, 19]-code), using construction X applied to Ce(17) ⊂ Ce(12) based on
- linear OA(6435, 4096, F64, 18) (dual of [4096, 4061, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(6425, 4096, F64, 13) (dual of [4096, 4071, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(644, 14, F64, 4) (dual of [14, 10, 5]-code or 14-arc in PG(3,64)), using
- discarding factors / shortening the dual code based on linear OA(644, 64, F64, 4) (dual of [64, 60, 5]-code or 64-arc in PG(3,64)), using
- Reed–Solomon code RS(60,64) [i]
- discarding factors / shortening the dual code based on linear OA(644, 64, F64, 4) (dual of [64, 60, 5]-code or 64-arc in PG(3,64)), 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(3247, 4110, S32, 18) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OOA(6439, 2096, F64, 2, 18) (dual of [(2096, 2), 4153, 19]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(6439, 2096, F64, 3, 18) (dual of [(2096, 3), 6249, 19]-NRT-code) | [i] | ||
| 4 | Digital (21, 39, 2096)-net over F64 | [i] | ||
| 5 | Linear OOA(6439, 2055, F64, 2, 18) (dual of [(2055, 2), 4071, 19]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(6439, 1370, F64, 3, 18) (dual of [(1370, 3), 4071, 19]-NRT-code) | [i] | ||