Information on Result #953992
Linear OOA(3193, 19687, F3, 3, 29) (dual of [(19687, 3), 58868, 30]-NRT-code), using OOA 3-folding based on linear OA(3193, 59061, F3, 29) (dual of [59061, 58868, 30]-code), using
- 2 times code embedding in larger space [i] based on linear OA(3191, 59059, F3, 29) (dual of [59059, 58868, 30]-code), using
- construction X applied to Ce(28) ⊂ Ce(27) [i] based on
- linear OA(3191, 59049, F3, 29) (dual of [59049, 58858, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(3181, 59049, F3, 28) (dual of [59049, 58868, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(30, 10, F3, 0) (dual of [10, 10, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(30, s, F3, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(28) ⊂ Ce(27) [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(3194, 19687, F3, 3, 29) (dual of [(19687, 3), 58867, 30]-NRT-code) | [i] | OOA Duplication | |
| 2 | Linear OOA(3193, 19687, F3, 4, 29) (dual of [(19687, 4), 78555, 30]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(3193, 19687, F3, 5, 29) (dual of [(19687, 5), 98242, 30]-NRT-code) | [i] | ||
| 4 | Digital (164, 193, 19687)-net over F3 | [i] | ||