Information on Result #731088
Linear OA(814, 8196, F8, 4) (dual of [8196, 8182, 5]-code), using trace code based on linear OA(647, 4098, F64, 4) (dual of [4098, 4091, 5]-code), using
- construction X applied to Ce(3) ⊂ Ce(2) [i] based on
- linear OA(647, 4096, F64, 4) (dual of [4096, 4089, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(645, 4096, F64, 3) (dual of [4096, 4091, 4]-code or 4096-cap in PG(4,64)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [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(815, 8197, F8, 4) (dual of [8197, 8182, 5]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(814, 8196, F8, 2, 4) (dual of [(8196, 2), 16378, 5]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(814, 8196, F8, 3, 4) (dual of [(8196, 3), 24574, 5]-NRT-code) | [i] | ||
| 4 | Linear OOA(814, 4098, F8, 2, 4) (dual of [(4098, 2), 8182, 5]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(814, 4098, F8, 3, 4) (dual of [(4098, 3), 12280, 5]-NRT-code) | [i] | OA Folding and Stacking | |