Information on Result #813907
Linear OOA(3118, 3291, F3, 2, 22) (dual of [(3291, 2), 6464, 23]-NRT-code), using OOA 2-folding based on linear OA(3118, 6582, F3, 22) (dual of [6582, 6464, 23]-code), using
- 1 times code embedding in larger space [i] based on linear OA(3117, 6581, F3, 22) (dual of [6581, 6464, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(18) [i] based on
- linear OA(3113, 6561, F3, 22) (dual of [6561, 6448, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(397, 6561, F3, 19) (dual of [6561, 6464, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(34, 20, F3, 2) (dual of [20, 16, 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(21) ⊂ Ce(18) [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(3118, 3226, F3, 3, 22) (dual of [(3226, 3), 9560, 23]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3118, 3226, F3, 4, 22) (dual of [(3226, 4), 12786, 23]-NRT-code) | [i] | ||
| 3 | Linear OOA(3118, 3226, F3, 5, 22) (dual of [(3226, 5), 16012, 23]-NRT-code) | [i] | ||
| 4 | Digital (96, 118, 3226)-net over F3 | [i] | ||