Information on Result #1302454
Linear OA(855, 8198, F8, 14) (dual of [8198, 8143, 15]-code), using construction X with Varšamov bound based on
- linear OA(854, 8196, F8, 14) (dual of [8196, 8142, 15]-code), using
- trace code [i] based on linear OA(6427, 4098, F64, 14) (dual of [4098, 4071, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(12) [i] 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
- construction X applied to Ce(13) ⊂ Ce(12) [i] based on
- trace code [i] based on linear OA(6427, 4098, F64, 14) (dual of [4098, 4071, 15]-code), using
- linear OA(854, 8197, F8, 13) (dual of [8197, 8143, 14]-code), using Gilbert–Varšamov bound and bm = 854 > Vbs−1(k−1) = 2 634237 917083 705149 649971 188156 376516 285541 156864 [i]
- linear OA(80, 1, F8, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(80, s, F8, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
Mode: 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 OOA(855, 8198, F8, 2, 14) (dual of [(8198, 2), 16341, 15]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(855, 8198, F8, 3, 14) (dual of [(8198, 3), 24539, 15]-NRT-code) | [i] | ||
| 3 | Digital (41, 55, 8198)-net over F8 | [i] | ||
| 4 | Linear OOA(855, 4099, F8, 2, 14) (dual of [(4099, 2), 8143, 15]-NRT-code) | [i] | OOA Folding | |