Information on Result #2678171
Linear OOA(3219, 59063, F3, 3, 29) (dual of [(59063, 3), 176970, 30]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(3216, 59062, F3, 3, 29) (dual of [(59062, 3), 176970, 30]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3216, 177186, F3, 29) (dual of [177186, 176970, 30]-code), using
- construction X applied to Ce(28) ⊂ Ce(24) [i] based on
- linear OA(3210, 177147, F3, 29) (dual of [177147, 176937, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(3177, 177147, F3, 25) (dual of [177147, 176970, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(36, 39, F3, 3) (dual of [39, 33, 4]-code or 39-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(28) ⊂ Ce(24) [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(3220, 59063, F3, 3, 29) (dual of [(59063, 3), 176969, 30]-NRT-code) | [i] | OOA Duplication | |
| 2 | Linear OOA(3219, 59063, F3, 4, 29) (dual of [(59063, 4), 236033, 30]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(3219, 59063, F3, 5, 29) (dual of [(59063, 5), 295096, 30]-NRT-code) | [i] | ||
| 4 | Digital (190, 219, 59063)-net over F3 | [i] | ||