Information on Result #1315714
Linear OA(6413, 4159, F64, 6) (dual of [4159, 4146, 7]-code), using 59 step Varšamov–Edel lengthening with (ri) = (2, 58 times 0) based on linear OA(6411, 4098, F64, 6) (dual of [4098, 4087, 7]-code), using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- linear OA(6411, 4096, F64, 6) (dual of [4096, 4085, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(649, 4096, F64, 5) (dual of [4096, 4087, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [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(6413, 4159, F64, 2, 6) (dual of [(4159, 2), 8305, 7]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(6413, 4159, F64, 3, 6) (dual of [(4159, 3), 12464, 7]-NRT-code) | [i] | ||
| 3 | Digital (7, 13, 4159)-net over F64 | [i] | ||
| 4 | Linear OOA(6413, 2079, F64, 2, 6) (dual of [(2079, 2), 4145, 7]-NRT-code) | [i] | OOA Folding | |