Information on Result #815140
Linear OOA(3183, 9847, F3, 2, 31) (dual of [(9847, 2), 19511, 32]-NRT-code), using OOA 2-folding based on linear OA(3183, 19694, F3, 31) (dual of [19694, 19511, 32]-code), using
- 1 times code embedding in larger space [i] based on linear OA(3182, 19693, F3, 31) (dual of [19693, 19511, 32]-code), using
- construction X applied to Ce(30) ⊂ Ce(28) [i] based on
- linear OA(3181, 19683, F3, 31) (dual of [19683, 19502, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(3172, 19683, F3, 29) (dual of [19683, 19511, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(31, 10, F3, 1) (dual of [10, 9, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to Ce(30) ⊂ Ce(28) [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(3183, 6831, F3, 3, 31) (dual of [(6831, 3), 20310, 32]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3183, 6831, F3, 4, 31) (dual of [(6831, 4), 27141, 32]-NRT-code) | [i] | ||
| 3 | Linear OOA(3183, 6831, F3, 5, 31) (dual of [(6831, 5), 33972, 32]-NRT-code) | [i] | ||
| 4 | Digital (152, 183, 6831)-net over F3 | [i] | ||