Information on Result #686334
Linear OA(891, 2097193, F8, 14) (dual of [2097193, 2097102, 15]-code), using construction X applied to Ce(13) ⊂ Ce(8) based on
- linear OA(885, 2097152, F8, 14) (dual of [2097152, 2097067, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(850, 2097152, F8, 9) (dual of [2097152, 2097102, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(86, 41, F8, 4) (dual of [41, 35, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(86, 56, F8, 4) (dual of [56, 50, 5]-code), using
- 1 times truncation [i] based on linear OA(87, 57, F8, 5) (dual of [57, 50, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(86, 56, F8, 4) (dual of [56, 50, 5]-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(892, 2097194, F8, 14) (dual of [2097194, 2097102, 15]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(893, 2097195, F8, 14) (dual of [2097195, 2097102, 15]-code) | [i] | ||
| 3 | Linear OA(894, 2097196, F8, 14) (dual of [2097196, 2097102, 15]-code) | [i] | ||
| 4 | Linear OA(895, 2097197, F8, 14) (dual of [2097197, 2097102, 15]-code) | [i] | ||
| 5 | Linear OOA(891, 2097193, F8, 2, 14) (dual of [(2097193, 2), 4194295, 15]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 6 | Linear OOA(891, 2097193, F8, 3, 14) (dual of [(2097193, 3), 6291488, 15]-NRT-code) | [i] | ||
| 7 | Digital (77, 91, 2097193)-net over F8 | [i] | ||
| 8 | Linear OA(892, 2097195, F8, 14) (dual of [2097195, 2097103, 15]-code) | [i] | Construction X with Varšamov Bound | |
| 9 | Linear OOA(891, 1048596, F8, 2, 14) (dual of [(1048596, 2), 2097101, 15]-NRT-code) | [i] | OOA Folding | |
| 10 | Linear OOA(891, 699064, F8, 3, 14) (dual of [(699064, 3), 2097101, 15]-NRT-code) | [i] | ||
| 11 | Linear OOA(891, 299599, F8, 14, 14) (dual of [(299599, 14), 4194295, 15]-NRT-code) | [i] | OA Folding and Stacking | |