Information on Result #953876
Linear OOA(3212, 59068, F3, 3, 28) (dual of [(59068, 3), 176992, 29]-NRT-code), using OOA 3-folding based on linear OA(3212, 177204, F3, 28) (dual of [177204, 176992, 29]-code), using
- 2 times code embedding in larger space [i] based on linear OA(3210, 177202, F3, 28) (dual of [177202, 176992, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(21) [i] based on
- linear OA(3199, 177147, F3, 28) (dual of [177147, 176948, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(3155, 177147, F3, 22) (dual of [177147, 176992, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(311, 55, F3, 5) (dual of [55, 44, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(311, 85, F3, 5) (dual of [85, 74, 6]-code), using
- construction X applied to Ce(27) ⊂ Ce(21) [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(3212, 59068, F3, 3, 27) (dual of [(59068, 3), 176992, 28]-NRT-code) | [i] | Strength Reduction for OOAs | |
| 2 | Linear OOA(3213, 59068, F3, 3, 28) (dual of [(59068, 3), 176991, 29]-NRT-code) | [i] | OOA Duplication | |
| 3 | Linear OOA(3214, 59068, F3, 3, 28) (dual of [(59068, 3), 176990, 29]-NRT-code) | [i] | ||
| 4 | Linear OOA(3212, 59068, F3, 4, 28) (dual of [(59068, 4), 236060, 29]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 5 | Linear OOA(3212, 59068, F3, 5, 28) (dual of [(59068, 5), 295128, 29]-NRT-code) | [i] | ||
| 6 | Digital (184, 212, 59068)-net over F3 | [i] | ||