Information on Result #686869
Linear OA(8142, 32799, F8, 31) (dual of [32799, 32657, 32]-code), using construction X applied to Ce(30) ⊂ Ce(25) 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(8111, 32768, F8, 26) (dual of [32768, 32657, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(86, 31, F8, 4) (dual of [31, 25, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(86, 56, F8, 4) (dual of [56, 50, 5]-code), using
- 1 times truncation [i] based on linear OA(87, 57, F8, 5) (dual of [57, 50, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(86, 56, F8, 4) (dual of [56, 50, 5]-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(8142, 32799, F8, 2, 31) (dual of [(32799, 2), 65456, 32]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(8142, 32799, F8, 3, 31) (dual of [(32799, 3), 98255, 32]-NRT-code) | [i] | ||
| 3 | Digital (111, 142, 32799)-net over F8 | [i] | ||
| 4 | Linear OOA(8142, 16399, F8, 2, 31) (dual of [(16399, 2), 32656, 32]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(8142, 10933, F8, 3, 31) (dual of [(10933, 3), 32657, 32]-NRT-code) | [i] | ||