Information on Result #1315716
Linear OA(6415, 4136, F64, 7) (dual of [4136, 4121, 8]-code), using 36 step Varšamov–Edel lengthening with (ri) = (2, 35 times 0) based on linear OA(6413, 4098, F64, 7) (dual of [4098, 4085, 8]-code), using
- construction X applied to Ce(6) ⊂ Ce(5) [i] based on
- linear OA(6413, 4096, F64, 7) (dual of [4096, 4083, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- 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(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 | OA(3218, 4136, S32, 7) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OOA(6415, 4136, F64, 2, 7) (dual of [(4136, 2), 8257, 8]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(6415, 4136, F64, 3, 7) (dual of [(4136, 3), 12393, 8]-NRT-code) | [i] | ||
| 4 | Digital (8, 15, 4136)-net over F64 | [i] | ||
| 5 | Linear OOA(6415, 2068, F64, 2, 7) (dual of [(2068, 2), 4121, 8]-NRT-code) | [i] | OOA Folding | |