Information on Result #2678348
Linear OOA(3204, 19687, F3, 3, 31) (dual of [(19687, 3), 58857, 32]-NRT-code), using 31 times duplication based on linear OOA(3203, 19687, F3, 3, 31) (dual of [(19687, 3), 58858, 32]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3203, 59061, F3, 31) (dual of [59061, 58858, 32]-code), using
- 1 times code embedding in larger space [i] based on linear OA(3202, 59060, F3, 31) (dual of [59060, 58858, 32]-code), using
- construction X applied to Ce(30) ⊂ Ce(28) [i] based on
- linear OA(3201, 59049, F3, 31) (dual of [59049, 58848, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- 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(31, 11, F3, 1) (dual of [11, 10, 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
- 1 times code embedding in larger space [i] based on linear OA(3202, 59060, F3, 31) (dual of [59060, 58858, 32]-code), using
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(3204, 19440, F3, 4, 31) (dual of [(19440, 4), 77556, 32]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3204, 19440, F3, 5, 31) (dual of [(19440, 5), 96996, 32]-NRT-code) | [i] | ||
| 3 | Digital (173, 204, 19440)-net over F3 | [i] | ||