Information on Result #1315972
Linear OA(6489, 4409, F64, 39) (dual of [4409, 4320, 40]-code), using 299 step Varšamov–Edel lengthening with (ri) = (6, 0, 1, 0, 0, 0, 1, 8 times 0, 1, 19 times 0, 1, 38 times 0, 1, 76 times 0, 1, 147 times 0) based on linear OA(6477, 4098, F64, 39) (dual of [4098, 4021, 40]-code), using
- construction X applied to Ce(38) ⊂ Ce(37) [i] based on
- linear OA(6477, 4096, F64, 39) (dual of [4096, 4019, 40]-code), using an extension Ce(38) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,38], and designed minimum distance d ≥ |I|+1 = 39 [i]
- linear OA(6475, 4096, F64, 38) (dual of [4096, 4021, 39]-code), using an extension Ce(37) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,37], and designed minimum distance d ≥ |I|+1 = 38 [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(6489, 4409, F64, 2, 39) (dual of [(4409, 2), 8729, 40]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(6489, 4409, F64, 3, 39) (dual of [(4409, 3), 13138, 40]-NRT-code) | [i] | ||
| 3 | Digital (50, 89, 4409)-net over F64 | [i] | ||
| 4 | Linear OOA(6489, 2204, F64, 2, 39) (dual of [(2204, 2), 4319, 40]-NRT-code) | [i] | OOA Folding | |