Information on Result #731097
Linear OA(830, 8196, F8, 8) (dual of [8196, 8166, 9]-code), using trace code based on linear OA(6415, 4098, F64, 8) (dual of [4098, 4083, 9]-code), using
- construction X applied to Ce(7) ⊂ Ce(6) [i] based on
- linear OA(6415, 4096, F64, 8) (dual of [4096, 4081, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- 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(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(831, 8197, F8, 8) (dual of [8197, 8166, 9]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(830, 8196, F8, 2, 8) (dual of [(8196, 2), 16362, 9]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(830, 8196, F8, 3, 8) (dual of [(8196, 3), 24558, 9]-NRT-code) | [i] | ||
| 4 | Digital (22, 30, 8196)-net over F8 | [i] | ||
| 5 | Linear OA(831, 8198, F8, 8) (dual of [8198, 8167, 9]-code) | [i] | Construction X with Varšamov Bound | |
| 6 | Linear OOA(830, 4098, F8, 2, 8) (dual of [(4098, 2), 8166, 9]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(830, 2732, F8, 3, 8) (dual of [(2732, 3), 8166, 9]-NRT-code) | [i] | ||
| 8 | Linear OOA(830, 2049, F8, 8, 8) (dual of [(2049, 8), 16362, 9]-NRT-code) | [i] | OA Folding and Stacking | |