Information on Result #686541
Linear OA(8158, 262181, F8, 29) (dual of [262181, 262023, 30]-code), using construction X applied to Ce(28) ⊂ Ce(22) based on
- linear OA(8151, 262144, F8, 29) (dual of [262144, 261993, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(8121, 262144, F8, 23) (dual of [262144, 262023, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [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(8159, 262182, F8, 29) (dual of [262182, 262023, 30]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(8160, 262183, F8, 29) (dual of [262183, 262023, 30]-code) | [i] | ||
| 3 | Linear OA(8161, 262184, F8, 29) (dual of [262184, 262023, 30]-code) | [i] | ||
| 4 | Linear OOA(8158, 262181, F8, 2, 29) (dual of [(262181, 2), 524204, 30]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 5 | Linear OOA(8158, 262181, F8, 3, 29) (dual of [(262181, 3), 786385, 30]-NRT-code) | [i] | ||
| 6 | Digital (129, 158, 262181)-net over F8 | [i] | ||
| 7 | Linear OA(8159, 262183, F8, 29) (dual of [262183, 262024, 30]-code) | [i] | Construction X with Varšamov Bound | |
| 8 | Linear OA(8160, 262185, F8, 29) (dual of [262185, 262025, 30]-code) | [i] | ||
| 9 | Linear OA(8161, 262187, F8, 29) (dual of [262187, 262026, 30]-code) | [i] | ||
| 10 | Linear OOA(8158, 131090, F8, 2, 29) (dual of [(131090, 2), 262022, 30]-NRT-code) | [i] | OOA Folding | |
| 11 | Linear OOA(8158, 87393, F8, 3, 29) (dual of [(87393, 3), 262021, 30]-NRT-code) | [i] | ||
| 12 | Linear OOA(8158, 18727, F8, 29, 29) (dual of [(18727, 29), 542925, 30]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |