Information on Result #686549
Linear OA(8110, 262181, F8, 20) (dual of [262181, 262071, 21]-code), using construction X applied to Ce(19) ⊂ Ce(13) based on
- linear OA(8103, 262144, F8, 20) (dual of [262144, 262041, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(873, 262144, F8, 14) (dual of [262144, 262071, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [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(8111, 262182, F8, 20) (dual of [262182, 262071, 21]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(8112, 262183, F8, 20) (dual of [262183, 262071, 21]-code) | [i] | ||
| 3 | Linear OA(8113, 262184, F8, 20) (dual of [262184, 262071, 21]-code) | [i] | ||
| 4 | Linear OOA(8110, 262181, F8, 2, 20) (dual of [(262181, 2), 524252, 21]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 5 | Linear OOA(8110, 262181, F8, 3, 20) (dual of [(262181, 3), 786433, 21]-NRT-code) | [i] | ||
| 6 | Digital (90, 110, 262181)-net over F8 | [i] | ||
| 7 | Linear OA(8111, 262183, F8, 20) (dual of [262183, 262072, 21]-code) | [i] | Construction X with Varšamov Bound | |
| 8 | Linear OA(8112, 262185, F8, 20) (dual of [262185, 262073, 21]-code) | [i] | ||
| 9 | Linear OOA(8110, 131090, F8, 2, 20) (dual of [(131090, 2), 262070, 21]-NRT-code) | [i] | OOA Folding | |
| 10 | Linear OOA(8110, 87393, F8, 3, 20) (dual of [(87393, 3), 262069, 21]-NRT-code) | [i] | ||
| 11 | Linear OOA(8110, 26218, F8, 20, 20) (dual of [(26218, 20), 524250, 21]-NRT-code) | [i] | OA Folding and Stacking | |