Information on Result #1315795
Linear OA(6448, 4869, F64, 20) (dual of [4869, 4821, 21]-code), using 762 step Varšamov–Edel lengthening with (ri) = (4, 0, 0, 1, 7 times 0, 1, 23 times 0, 1, 70 times 0, 1, 189 times 0, 1, 465 times 0) based on linear OA(6439, 4098, F64, 20) (dual of [4098, 4059, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(18) [i] based on
- linear OA(6439, 4096, F64, 20) (dual of [4096, 4057, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(6437, 4096, F64, 19) (dual of [4096, 4059, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(640, 2, F64, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(640, s, F64, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
Mode: 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(6448, 4869, F64, 2, 20) (dual of [(4869, 2), 9690, 21]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(6448, 4869, F64, 3, 20) (dual of [(4869, 3), 14559, 21]-NRT-code) | [i] | ||
| 3 | Digital (28, 48, 4869)-net over F64 | [i] | ||
| 4 | Linear OOA(6448, 2434, F64, 2, 20) (dual of [(2434, 2), 4820, 21]-NRT-code) | [i] | OOA Folding | |