Information on Result #686330
Linear OA(8120, 2097194, F8, 19) (dual of [2097194, 2097074, 20]-code), using construction X applied to Ce(18) ⊂ Ce(12) based on
- linear OA(8113, 2097152, F8, 19) (dual of [2097152, 2097039, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(878, 2097152, F8, 13) (dual of [2097152, 2097074, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(87, 42, F8, 5) (dual of [42, 35, 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(8121, 2097195, F8, 19) (dual of [2097195, 2097074, 20]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(8122, 2097196, F8, 19) (dual of [2097196, 2097074, 20]-code) | [i] | ||
| 3 | Linear OA(8123, 2097197, F8, 19) (dual of [2097197, 2097074, 20]-code) | [i] | ||
| 4 | Linear OOA(8120, 2097194, F8, 2, 19) (dual of [(2097194, 2), 4194268, 20]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 5 | Linear OOA(8120, 2097194, F8, 3, 19) (dual of [(2097194, 3), 6291462, 20]-NRT-code) | [i] | ||
| 6 | Digital (101, 120, 2097194)-net over F8 | [i] | ||
| 7 | Linear OA(8121, 2097196, F8, 19) (dual of [2097196, 2097075, 20]-code) | [i] | Construction X with Varšamov Bound | |
| 8 | Linear OA(8122, 2097198, F8, 19) (dual of [2097198, 2097076, 20]-code) | [i] | ||
| 9 | Linear OA(8123, 2097200, F8, 19) (dual of [2097200, 2097077, 20]-code) | [i] | ||
| 10 | Linear OOA(8120, 1048597, F8, 2, 19) (dual of [(1048597, 2), 2097074, 20]-NRT-code) | [i] | OOA Folding | |
| 11 | Linear OOA(8120, 699064, F8, 3, 19) (dual of [(699064, 3), 2097072, 20]-NRT-code) | [i] | ||
| 12 | Linear OOA(8120, 233021, F8, 19, 19) (dual of [(233021, 19), 4427279, 20]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |