Information on Result #813684
Linear OOA(3123, 9853, F3, 2, 20) (dual of [(9853, 2), 19583, 21]-NRT-code), using OOA 2-folding based on linear OA(3123, 19706, F3, 20) (dual of [19706, 19583, 21]-code), using
- 1 times code embedding in larger space [i] based on linear OA(3122, 19705, F3, 20) (dual of [19705, 19583, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(16) [i] based on
- linear OA(3118, 19683, F3, 20) (dual of [19683, 19565, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(3100, 19683, F3, 17) (dual of [19683, 19583, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [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(19) ⊂ Ce(16) [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(3123, 8915, F3, 3, 20) (dual of [(8915, 3), 26622, 21]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3123, 8915, F3, 4, 20) (dual of [(8915, 4), 35537, 21]-NRT-code) | [i] | ||
| 3 | Linear OOA(3123, 8915, F3, 5, 20) (dual of [(8915, 5), 44452, 21]-NRT-code) | [i] | ||
| 4 | Digital (103, 123, 8915)-net over F3 | [i] | ||