Information on Result #698726
Linear OA(6443, 4098, F64, 22) (dual of [4098, 4055, 23]-code), using construction X applied to Ce(21) ⊂ Ce(20) based on
- linear OA(6443, 4096, F64, 22) (dual of [4096, 4053, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(6441, 4096, F64, 21) (dual of [4096, 4055, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [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(886, 8196, F8, 22) (dual of [8196, 8110, 23]-code) | [i] | Trace Code | |
| 2 | OA(3252, 4098, S32, 22) | [i] | Discarding Parts of the Base for OAs | |
| 3 | Linear OA(6454, 4163, F64, 22) (dual of [4163, 4109, 23]-code) | [i] | (u, u+v)-Construction | |
| 4 | Linear OA(6455, 4178, F64, 22) (dual of [4178, 4123, 23]-code) | [i] | ||
| 5 | Linear OA(6456, 4180, F64, 22) (dual of [4180, 4124, 23]-code) | [i] | ||
| 6 | Linear OA(6457, 4202, F64, 22) (dual of [4202, 4145, 23]-code) | [i] | ||
| 7 | Linear OA(6458, 4204, F64, 22) (dual of [4204, 4146, 23]-code) | [i] | ||
| 8 | Linear OA(6459, 4228, F64, 22) (dual of [4228, 4169, 23]-code) | [i] | ||
| 9 | Linear OA(6460, 4243, F64, 22) (dual of [4243, 4183, 23]-code) | [i] | ||
| 10 | Linear OA(6461, 4295, F64, 22) (dual of [4295, 4234, 23]-code) | [i] | ||
| 11 | Linear OA(6462, 4415, F64, 22) (dual of [4415, 4353, 23]-code) | [i] | ||
| 12 | Linear OA(6449, 4120, F64, 22) (dual of [4120, 4071, 23]-code) | [i] | Varšamov–Edel Lengthening | |
| 13 | Linear OA(6450, 4157, F64, 22) (dual of [4157, 4107, 23]-code) | [i] | ||
| 14 | Linear OA(6451, 4259, F64, 22) (dual of [4259, 4208, 23]-code) | [i] | ||
| 15 | Linear OA(6452, 4522, F64, 22) (dual of [4522, 4470, 23]-code) | [i] | ||
| 16 | Linear OA(6453, 5109, F64, 22) (dual of [5109, 5056, 23]-code) | [i] | ||
| 17 | Linear OOA(6443, 2049, F64, 2, 22) (dual of [(2049, 2), 4055, 23]-NRT-code) | [i] | OOA Folding | |
| 18 | Linear OOA(6443, 1366, F64, 3, 22) (dual of [(1366, 3), 4055, 23]-NRT-code) | [i] | ||