Information on Result #686540
Linear OA(8163, 262180, F8, 30) (dual of [262180, 262017, 31]-code), using construction X applied to Ce(29) ⊂ Ce(24) based on
- linear OA(8157, 262144, F8, 30) (dual of [262144, 261987, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(8127, 262144, F8, 25) (dual of [262144, 262017, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(86, 36, F8, 4) (dual of [36, 30, 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 OA(8164, 262181, F8, 30) (dual of [262181, 262017, 31]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(8165, 262182, F8, 30) (dual of [262182, 262017, 31]-code) | [i] | ||
| 3 | Linear OA(8166, 262183, F8, 30) (dual of [262183, 262017, 31]-code) | [i] | ||
| 4 | Linear OA(8167, 262184, F8, 30) (dual of [262184, 262017, 31]-code) | [i] | ||
| 5 | Linear OOA(8163, 262180, F8, 2, 30) (dual of [(262180, 2), 524197, 31]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 6 | Linear OOA(8163, 262180, F8, 3, 30) (dual of [(262180, 3), 786377, 31]-NRT-code) | [i] | ||
| 7 | Digital (133, 163, 262180)-net over F8 | [i] | ||
| 8 | Linear OA(8164, 262182, F8, 30) (dual of [262182, 262018, 31]-code) | [i] | Construction X with Varšamov Bound | |
| 9 | Linear OA(8165, 262184, F8, 30) (dual of [262184, 262019, 31]-code) | [i] | ||
| 10 | Linear OA(8166, 262186, F8, 30) (dual of [262186, 262020, 31]-code) | [i] | ||
| 11 | Linear OOA(8163, 131090, F8, 2, 30) (dual of [(131090, 2), 262017, 31]-NRT-code) | [i] | OOA Folding | |
| 12 | Linear OOA(8163, 87393, F8, 3, 30) (dual of [(87393, 3), 262016, 31]-NRT-code) | [i] | ||