Information on Result #686647
Linear OA(8165, 32793, F8, 37) (dual of [32793, 32628, 38]-code), using construction X applied to C([0,18]) ⊂ C([0,16]) based on
- linear OA(8161, 32769, F8, 37) (dual of [32769, 32608, 38]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769 | 810−1, defining interval I = [0,18], and minimum distance d ≥ |{−18,−17,…,18}|+1 = 38 (BCH-bound) [i]
- linear OA(8141, 32769, F8, 33) (dual of [32769, 32628, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769 | 810−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
- linear OA(84, 24, F8, 3) (dual of [24, 20, 4]-code or 24-cap in PG(3,8)), 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(8166, 32794, F8, 37) (dual of [32794, 32628, 38]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(8167, 32795, F8, 37) (dual of [32795, 32628, 38]-code) | [i] | ||
| 3 | Linear OOA(8165, 32793, F8, 2, 37) (dual of [(32793, 2), 65421, 38]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(8165, 32793, F8, 3, 37) (dual of [(32793, 3), 98214, 38]-NRT-code) | [i] | ||
| 5 | Digital (128, 165, 32793)-net over F8 | [i] | ||
| 6 | Linear OA(8166, 32795, F8, 37) (dual of [32795, 32629, 38]-code) | [i] | Construction X with Varšamov Bound | |
| 7 | Linear OA(8167, 32797, F8, 37) (dual of [32797, 32630, 38]-code) | [i] | ||
| 8 | Linear OOA(8165, 16396, F8, 2, 37) (dual of [(16396, 2), 32627, 38]-NRT-code) | [i] | OOA Folding | |
| 9 | Linear OOA(8165, 10931, F8, 3, 37) (dual of [(10931, 3), 32628, 38]-NRT-code) | [i] | ||