Information on Result #814875
Linear OOA(3177, 9853, F3, 2, 29) (dual of [(9853, 2), 19529, 30]-NRT-code), using OOA 2-folding based on linear OA(3177, 19706, F3, 29) (dual of [19706, 19529, 30]-code), using
- 1 times code embedding in larger space [i] based on linear OA(3176, 19705, F3, 29) (dual of [19705, 19529, 30]-code), using
- construction X applied to Ce(28) ⊂ Ce(25) [i] based on
- 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(3154, 19683, F3, 26) (dual of [19683, 19529, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(34, 22, F3, 2) (dual of [22, 18, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(34, 40, F3, 2) (dual of [40, 36, 3]-code), using
- Hamming code H(4,3) [i]
- discarding factors / shortening the dual code based on linear OA(34, 40, F3, 2) (dual of [40, 36, 3]-code), using
- construction X applied to Ce(28) ⊂ Ce(25) [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(3177, 8558, F3, 3, 29) (dual of [(8558, 3), 25497, 30]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3177, 8558, F3, 4, 29) (dual of [(8558, 4), 34055, 30]-NRT-code) | [i] | ||
| 3 | Linear OOA(3177, 8558, F3, 5, 29) (dual of [(8558, 5), 42613, 30]-NRT-code) | [i] | ||
| 4 | Digital (148, 177, 8558)-net over F3 | [i] | ||