Information on Result #1302568
Linear OA(875, 8198, F8, 19) (dual of [8198, 8123, 20]-code), using construction X with Varšamov bound based on
- linear OA(874, 8196, F8, 19) (dual of [8196, 8122, 20]-code), using
- trace code [i] based on linear OA(6437, 4098, F64, 19) (dual of [4098, 4061, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(17) [i] based on
- linear OA(6437, 4096, F64, 19) (dual of [4096, 4059, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(6435, 4096, F64, 18) (dual of [4096, 4061, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [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(18) ⊂ Ce(17) [i] based on
- trace code [i] based on linear OA(6437, 4098, F64, 19) (dual of [4098, 4061, 20]-code), using
- linear OA(874, 8197, F8, 18) (dual of [8197, 8123, 19]-code), using Gilbert–Varšamov bound and bm = 874 > Vbs−1(k−1) = 2 186497 457217 122394 473217 950324 453710 912907 841059 381144 778470 950400 [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(875, 8198, F8, 2, 19) (dual of [(8198, 2), 16321, 20]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(875, 8198, F8, 3, 19) (dual of [(8198, 3), 24519, 20]-NRT-code) | [i] | ||
| 3 | Digital (56, 75, 8198)-net over F8 | [i] | ||
| 4 | Linear OOA(875, 4099, F8, 2, 19) (dual of [(4099, 2), 8123, 20]-NRT-code) | [i] | OOA Folding | |