Information on Result #731157
Linear OA(886, 8196, F8, 22) (dual of [8196, 8110, 23]-code), using trace code based on linear OA(6443, 4098, F64, 22) (dual of [4098, 4055, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(20) [i] 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(887, 8197, F8, 22) (dual of [8197, 8110, 23]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(887, 8198, F8, 22) (dual of [8198, 8111, 23]-code) | [i] | Construction X with Varšamov Bound | |
| 3 | Linear OOA(886, 4098, F8, 2, 22) (dual of [(4098, 2), 8110, 23]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(886, 2732, F8, 3, 22) (dual of [(2732, 3), 8110, 23]-NRT-code) | [i] | ||
| 5 | Linear OOA(886, 745, F8, 22, 22) (dual of [(745, 22), 16304, 23]-NRT-code) | [i] | OA Folding and Stacking | |