Information on Result #1302550
Linear OA(871, 8198, F8, 18) (dual of [8198, 8127, 19]-code), using construction X with Varšamov bound based on
- linear OA(870, 8196, F8, 18) (dual of [8196, 8126, 19]-code), using
- trace code [i] based on linear OA(6435, 4098, F64, 18) (dual of [4098, 4063, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(16) [i] based on
- 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(6433, 4096, F64, 17) (dual of [4096, 4063, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [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(17) ⊂ Ce(16) [i] based on
- trace code [i] based on linear OA(6435, 4098, F64, 18) (dual of [4098, 4063, 19]-code), using
- linear OA(870, 8197, F8, 17) (dual of [8197, 8127, 18]-code), using Gilbert–Varšamov bound and bm = 870 > Vbs−1(k−1) = 649 140869 377289 573886 415146 843877 583999 433758 379323 704041 274880 [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(871, 8198, F8, 2, 18) (dual of [(8198, 2), 16325, 19]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(871, 8198, F8, 3, 18) (dual of [(8198, 3), 24523, 19]-NRT-code) | [i] | ||
| 3 | Digital (53, 71, 8198)-net over F8 | [i] | ||
| 4 | Linear OOA(871, 4099, F8, 2, 18) (dual of [(4099, 2), 8127, 19]-NRT-code) | [i] | OOA Folding | |