Information on Result #815126
Linear OOA(3165, 3290, F3, 2, 31) (dual of [(3290, 2), 6415, 32]-NRT-code), using OOA 2-folding based on linear OA(3165, 6580, F3, 31) (dual of [6580, 6415, 32]-code), using
- discarding factors / shortening the dual code based on linear OA(3165, 6581, F3, 31) (dual of [6581, 6416, 32]-code), using
- construction X applied to Ce(30) ⊂ Ce(27) [i] based on
- linear OA(3161, 6561, F3, 31) (dual of [6561, 6400, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(3145, 6561, F3, 28) (dual of [6561, 6416, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [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(30) ⊂ 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(3165, 3290, F3, 3, 31) (dual of [(3290, 3), 9705, 32]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3165, 3290, F3, 4, 31) (dual of [(3290, 4), 12995, 32]-NRT-code) | [i] | ||
| 3 | Linear OOA(3165, 3290, F3, 5, 31) (dual of [(3290, 5), 16285, 32]-NRT-code) | [i] | ||
| 4 | Digital (134, 165, 3290)-net over F3 | [i] | ||