Information on Result #686547
Linear OA(8121, 262180, F8, 22) (dual of [262180, 262059, 23]-code), using construction X applied to Ce(21) ⊂ Ce(16) based on
- linear OA(8115, 262144, F8, 22) (dual of [262144, 262029, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(885, 262144, F8, 17) (dual of [262144, 262059, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [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(8122, 262181, F8, 22) (dual of [262181, 262059, 23]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(8123, 262182, F8, 22) (dual of [262182, 262059, 23]-code) | [i] | ||
| 3 | Linear OA(8124, 262183, F8, 22) (dual of [262183, 262059, 23]-code) | [i] | ||
| 4 | Linear OA(8125, 262184, F8, 22) (dual of [262184, 262059, 23]-code) | [i] | ||
| 5 | Linear OOA(8121, 262180, F8, 2, 22) (dual of [(262180, 2), 524239, 23]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 6 | Linear OOA(8121, 262180, F8, 3, 22) (dual of [(262180, 3), 786419, 23]-NRT-code) | [i] | ||
| 7 | Digital (99, 121, 262180)-net over F8 | [i] | ||
| 8 | Linear OA(8122, 262182, F8, 22) (dual of [262182, 262060, 23]-code) | [i] | Construction X with Varšamov Bound | |
| 9 | Linear OA(8123, 262184, F8, 22) (dual of [262184, 262061, 23]-code) | [i] | ||
| 10 | Linear OOA(8121, 131090, F8, 2, 22) (dual of [(131090, 2), 262059, 23]-NRT-code) | [i] | OOA Folding | |
| 11 | Linear OOA(8121, 87393, F8, 3, 22) (dual of [(87393, 3), 262058, 23]-NRT-code) | [i] | ||