Information on Result #813158
Linear OOA(381, 3284, F3, 2, 15) (dual of [(3284, 2), 6487, 16]-NRT-code), using OOA 2-folding based on linear OA(381, 6568, F3, 15) (dual of [6568, 6487, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(381, 6569, F3, 15) (dual of [6569, 6488, 16]-code), using
- 1 times truncation [i] based on linear OA(382, 6570, F3, 16) (dual of [6570, 6488, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(13) [i] based on
- linear OA(381, 6561, F3, 16) (dual of [6561, 6480, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(373, 6561, F3, 14) (dual of [6561, 6488, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [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
- construction X applied to Ce(15) ⊂ Ce(13) [i] based on
- 1 times truncation [i] based on linear OA(382, 6570, F3, 16) (dual of [6570, 6488, 17]-code), 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(381, 3284, F3, 3, 15) (dual of [(3284, 3), 9771, 16]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(381, 3284, F3, 4, 15) (dual of [(3284, 4), 13055, 16]-NRT-code) | [i] | ||
| 3 | Linear OOA(381, 3284, F3, 5, 15) (dual of [(3284, 5), 16339, 16]-NRT-code) | [i] | ||
| 4 | Digital (66, 81, 3284)-net over F3 | [i] | ||