Information on Result #675354
Linear OA(3249, 6602, F3, 44) (dual of [6602, 6353, 45]-code), using construction X applied to C([0,22]) ⊂ C([0,19]) based on
- linear OA(3241, 6562, F3, 45) (dual of [6562, 6321, 46]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 316−1, defining interval I = [0,22], and minimum distance d ≥ |{−22,−21,…,22}|+1 = 46 (BCH-bound) [i]
- linear OA(3209, 6562, F3, 39) (dual of [6562, 6353, 40]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 316−1, defining interval I = [0,19], and minimum distance d ≥ |{−19,−18,…,19}|+1 = 40 (BCH-bound) [i]
- linear OA(38, 40, F3, 4) (dual of [40, 32, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(38, 41, F3, 4) (dual of [41, 33, 5]-code), using
- the narrow-sense BCH-code C(I) with length 41 | 38−1, defining interval I = [1,1], and minimum distance d ≥ |{−3,−1,1,3}|+1 = 5 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(38, 41, F3, 4) (dual of [41, 33, 5]-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(3249, 5381, F3, 2, 44) (dual of [(5381, 2), 10513, 45]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3249, 5381, F3, 3, 44) (dual of [(5381, 3), 15894, 45]-NRT-code) | [i] | ||
| 3 | Linear OOA(3249, 5381, F3, 4, 44) (dual of [(5381, 4), 21275, 45]-NRT-code) | [i] | ||
| 4 | Linear OOA(3249, 5381, F3, 5, 44) (dual of [(5381, 5), 26656, 45]-NRT-code) | [i] | ||
| 5 | Digital (205, 249, 5381)-net over F3 | [i] | ||