Information on Result #815509
Linear OOA(3178, 3285, F3, 2, 34) (dual of [(3285, 2), 6392, 35]-NRT-code), using OOA 2-folding based on linear OA(3178, 6570, F3, 34) (dual of [6570, 6392, 35]-code), using
- construction X applied to Ce(33) ⊂ Ce(31) [i] based on
- linear OA(3177, 6561, F3, 34) (dual of [6561, 6384, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(3169, 6561, F3, 32) (dual of [6561, 6392, 33]-code), using an extension Ce(31) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,31], and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(31, 9, F3, 1) (dual of [9, 8, 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
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(3178, 3146, F3, 3, 34) (dual of [(3146, 3), 9260, 35]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3178, 3146, F3, 4, 34) (dual of [(3146, 4), 12406, 35]-NRT-code) | [i] | ||
| 3 | Linear OOA(3178, 3146, F3, 5, 34) (dual of [(3146, 5), 15552, 35]-NRT-code) | [i] | ||
| 4 | Digital (144, 178, 3146)-net over F3 | [i] | ||