Information on Result #1302667
Linear OA(899, 8198, F8, 25) (dual of [8198, 8099, 26]-code), using construction X with Varšamov bound based on
- linear OA(898, 8196, F8, 25) (dual of [8196, 8098, 26]-code), using
- trace code [i] based on linear OA(6449, 4098, F64, 25) (dual of [4098, 4049, 26]-code), using
- construction X applied to Ce(24) ⊂ Ce(23) [i] based on
- linear OA(6449, 4096, F64, 25) (dual of [4096, 4047, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(6447, 4096, F64, 24) (dual of [4096, 4049, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [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(24) ⊂ Ce(23) [i] based on
- trace code [i] based on linear OA(6449, 4098, F64, 25) (dual of [4098, 4049, 26]-code), using
- linear OA(898, 8197, F8, 24) (dual of [8197, 8099, 25]-code), using Gilbert–Varšamov bound and bm = 898 > Vbs−1(k−1) = 1057 697660 867625 201199 791430 148465 878654 408009 926046 102126 324849 486775 664006 889012 348928 [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(899, 8198, F8, 2, 25) (dual of [(8198, 2), 16297, 26]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(899, 8198, F8, 3, 25) (dual of [(8198, 3), 24495, 26]-NRT-code) | [i] | ||
| 3 | Digital (74, 99, 8198)-net over F8 | [i] | ||
| 4 | Linear OOA(899, 4099, F8, 2, 25) (dual of [(4099, 2), 8099, 26]-NRT-code) | [i] | OOA Folding | |