Information on Result #686550
Linear OA(8104, 262181, F8, 19) (dual of [262181, 262077, 20]-code), using construction X applied to Ce(18) ⊂ Ce(12) based on
- linear OA(897, 262144, F8, 19) (dual of [262144, 262047, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(867, 262144, F8, 13) (dual of [262144, 262077, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [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(8105, 262182, F8, 19) (dual of [262182, 262077, 20]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(8106, 262183, F8, 19) (dual of [262183, 262077, 20]-code) | [i] | ||
| 3 | Linear OA(8107, 262184, F8, 19) (dual of [262184, 262077, 20]-code) | [i] | ||
| 4 | Linear OOA(8104, 262181, F8, 2, 19) (dual of [(262181, 2), 524258, 20]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 5 | Linear OOA(8104, 262181, F8, 3, 19) (dual of [(262181, 3), 786439, 20]-NRT-code) | [i] | ||
| 6 | Digital (85, 104, 262181)-net over F8 | [i] | ||
| 7 | Linear OA(8105, 262183, F8, 19) (dual of [262183, 262078, 20]-code) | [i] | Construction X with Varšamov Bound | |
| 8 | Linear OA(8106, 262185, F8, 19) (dual of [262185, 262079, 20]-code) | [i] | ||
| 9 | Linear OA(8107, 262187, F8, 19) (dual of [262187, 262080, 20]-code) | [i] | ||
| 10 | Linear OOA(8104, 131090, F8, 2, 19) (dual of [(131090, 2), 262076, 20]-NRT-code) | [i] | OOA Folding | |
| 11 | Linear OOA(8104, 87393, F8, 3, 19) (dual of [(87393, 3), 262075, 20]-NRT-code) | [i] | ||
| 12 | Linear OOA(8104, 29131, F8, 19, 19) (dual of [(29131, 19), 553385, 20]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |