Information on Result #686542
Linear OA(8152, 262181, F8, 28) (dual of [262181, 262029, 29]-code), using construction X applied to Ce(27) ⊂ Ce(21) based on
- linear OA(8145, 262144, F8, 28) (dual of [262144, 261999, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- 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(87, 37, F8, 5) (dual of [37, 30, 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(8153, 262182, F8, 28) (dual of [262182, 262029, 29]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(8154, 262183, F8, 28) (dual of [262183, 262029, 29]-code) | [i] | ||
| 3 | Linear OA(8155, 262184, F8, 28) (dual of [262184, 262029, 29]-code) | [i] | ||
| 4 | Linear OOA(8152, 262181, F8, 2, 28) (dual of [(262181, 2), 524210, 29]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 5 | Linear OOA(8152, 262181, F8, 3, 28) (dual of [(262181, 3), 786391, 29]-NRT-code) | [i] | ||
| 6 | Digital (124, 152, 262181)-net over F8 | [i] | ||
| 7 | Linear OA(8153, 262183, F8, 28) (dual of [262183, 262030, 29]-code) | [i] | Construction X with Varšamov Bound | |
| 8 | Linear OA(8154, 262185, F8, 28) (dual of [262185, 262031, 29]-code) | [i] | ||
| 9 | Linear OA(8155, 262187, F8, 28) (dual of [262187, 262032, 29]-code) | [i] | ||
| 10 | Linear OOA(8152, 131090, F8, 2, 28) (dual of [(131090, 2), 262028, 29]-NRT-code) | [i] | OOA Folding | |
| 11 | Linear OOA(8152, 87393, F8, 3, 28) (dual of [(87393, 3), 262027, 29]-NRT-code) | [i] | ||
| 12 | Linear OOA(8152, 18727, F8, 28, 28) (dual of [(18727, 28), 524204, 29]-NRT-code) | [i] | OA Folding and Stacking | |