Information on Result #1302683
Linear OA(8103, 8198, F8, 26) (dual of [8198, 8095, 27]-code), using construction X with Varšamov bound based on
- linear OA(8102, 8196, F8, 26) (dual of [8196, 8094, 27]-code), using
- trace code [i] based on linear OA(6451, 4098, F64, 26) (dual of [4098, 4047, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(24) [i] based on
- linear OA(6451, 4096, F64, 26) (dual of [4096, 4045, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- 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(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(25) ⊂ Ce(24) [i] based on
- trace code [i] based on linear OA(6451, 4098, F64, 26) (dual of [4098, 4047, 27]-code), using
- linear OA(8102, 8197, F8, 25) (dual of [8197, 8095, 26]-code), using Gilbert–Varšamov bound and bm = 8102 > Vbs−1(k−1) = 2 521375 082338 364456 404226 842126 278738 853375 056216 413534 096799 626528 764135 982447 256885 859328 [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(8103, 8198, F8, 2, 26) (dual of [(8198, 2), 16293, 27]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(8103, 8198, F8, 3, 26) (dual of [(8198, 3), 24491, 27]-NRT-code) | [i] | ||
| 3 | Digital (77, 103, 8198)-net over F8 | [i] | ||
| 4 | Linear OOA(8103, 4099, F8, 2, 26) (dual of [(4099, 2), 8095, 27]-NRT-code) | [i] | OOA Folding | |