Information on Result #813100
Linear OOA(3116, 265742, F3, 2, 14) (dual of [(265742, 2), 531368, 15]-NRT-code), using OOA 2-folding based on linear OA(3116, 531484, F3, 14) (dual of [531484, 531368, 15]-code), using
- 1 times code embedding in larger space [i] based on linear OA(3115, 531483, F3, 14) (dual of [531483, 531368, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(9) [i] based on
- linear OA(3109, 531441, F3, 14) (dual of [531441, 531332, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(373, 531441, F3, 10) (dual of [531441, 531368, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(36, 42, F3, 3) (dual of [42, 36, 4]-code or 42-cap in PG(5,3)), using
- discarding factors / shortening the dual code based on linear OA(36, 48, F3, 3) (dual of [48, 42, 4]-code or 48-cap in PG(5,3)), using
- construction X applied to Ce(13) ⊂ Ce(9) [i] based on
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 OOA(3117, 265742, F3, 2, 14) (dual of [(265742, 2), 531367, 15]-NRT-code) | [i] | OOA Duplication | |
| 2 | Linear OOA(3116, 216110, F3, 3, 14) (dual of [(216110, 3), 648214, 15]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(3116, 216110, F3, 4, 14) (dual of [(216110, 4), 864324, 15]-NRT-code) | [i] | ||
| 4 | Linear OOA(3116, 216110, F3, 5, 14) (dual of [(216110, 5), 1080434, 15]-NRT-code) | [i] | ||
| 5 | Digital (102, 116, 216110)-net over F3 | [i] | ||