Information on Result #686872
Linear OA(8128, 32800, F8, 28) (dual of [32800, 32672, 29]-code), using construction X applied to Ce(27) ⊂ Ce(21) based on
- 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(896, 32768, F8, 22) (dual of [32768, 32672, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(87, 32, F8, 5) (dual of [32, 25, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(87, 57, F8, 5) (dual of [57, 50, 6]-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 OA(8129, 32801, F8, 28) (dual of [32801, 32672, 29]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(8130, 32802, F8, 28) (dual of [32802, 32672, 29]-code) | [i] | ||
| 3 | Linear OOA(8128, 32800, F8, 2, 28) (dual of [(32800, 2), 65472, 29]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(8128, 32800, F8, 3, 28) (dual of [(32800, 3), 98272, 29]-NRT-code) | [i] | ||
| 5 | Digital (100, 128, 32800)-net over F8 | [i] | ||
| 6 | Linear OA(8129, 32802, F8, 28) (dual of [32802, 32673, 29]-code) | [i] | Construction X with Varšamov Bound | |
| 7 | Linear OOA(8128, 16400, F8, 2, 28) (dual of [(16400, 2), 32672, 29]-NRT-code) | [i] | OOA Folding | |
| 8 | Linear OOA(8128, 10933, F8, 3, 28) (dual of [(10933, 3), 32671, 29]-NRT-code) | [i] | ||