Information on Result #698738
Linear OA(6427, 4098, F64, 14) (dual of [4098, 4071, 15]-code), using construction X applied to Ce(13) ⊂ Ce(12) based on
- linear OA(6427, 4096, F64, 14) (dual of [4096, 4069, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [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(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: 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 | Linear OA(854, 8196, F8, 14) (dual of [8196, 8142, 15]-code) | [i] | Trace Code | |
| 2 | OA(3233, 4098, S32, 14) | [i] | Discarding Parts of the Base for OAs | |
| 3 | Linear OA(6434, 4163, F64, 14) (dual of [4163, 4129, 15]-code) | [i] | (u, u+v)-Construction | |
| 4 | Linear OA(6435, 4178, F64, 14) (dual of [4178, 4143, 15]-code) | [i] | ||
| 5 | Linear OA(6436, 4180, F64, 14) (dual of [4180, 4144, 15]-code) | [i] | ||
| 6 | Linear OA(6437, 4228, F64, 14) (dual of [4228, 4191, 15]-code) | [i] | ||
| 7 | Linear OA(6438, 4293, F64, 14) (dual of [4293, 4255, 15]-code) | [i] | ||
| 8 | Linear OA(6431, 4118, F64, 14) (dual of [4118, 4087, 15]-code) | [i] | Varšamov–Edel Lengthening | |
| 9 | Linear OA(6432, 4173, F64, 14) (dual of [4173, 4141, 15]-code) | [i] | ||
| 10 | Linear OA(6433, 4382, F64, 14) (dual of [4382, 4349, 15]-code) | [i] | ||
| 11 | Linear OA(6434, 5061, F64, 14) (dual of [5061, 5027, 15]-code) | [i] | ||
| 12 | Linear OOA(6427, 2049, F64, 2, 14) (dual of [(2049, 2), 4071, 15]-NRT-code) | [i] | OOA Folding | |
| 13 | Linear OOA(6427, 1366, F64, 3, 14) (dual of [(1366, 3), 4071, 15]-NRT-code) | [i] | ||