Information on Result #686809
Linear OA(8139, 32786, F8, 31) (dual of [32786, 32647, 32]-code), using construction X applied to Ce(30) ⊂ Ce(27) based on
- linear OA(8136, 32768, F8, 31) (dual of [32768, 32632, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(8121, 32768, F8, 28) (dual of [32768, 32647, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(83, 18, F8, 2) (dual of [18, 15, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(83, 63, F8, 2) (dual of [63, 60, 3]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 82−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 3 [i]
- discarding factors / shortening the dual code based on linear OA(83, 63, F8, 2) (dual of [63, 60, 3]-code), using
Mode: Constructive and 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(8139, 32786, F8, 2, 31) (dual of [(32786, 2), 65433, 32]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(8139, 32786, F8, 3, 31) (dual of [(32786, 3), 98219, 32]-NRT-code) | [i] | ||
| 3 | Digital (108, 139, 32786)-net over F8 | [i] | ||
| 4 | Linear OOA(8139, 16393, F8, 2, 31) (dual of [(16393, 2), 32647, 32]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(8139, 10928, F8, 3, 31) (dual of [(10928, 3), 32645, 32]-NRT-code) | [i] | ||