Information on Result #2266787
Linear OA(3227, 6628, F3, 39) (dual of [6628, 6401, 40]-code), using 2 times code embedding in larger space based on linear OA(3225, 6626, F3, 39) (dual of [6626, 6401, 40]-code), using
- construction X applied to C([0,19]) ⊂ C([0,15]) [i] based on
- 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(3161, 6562, F3, 31) (dual of [6562, 6401, 32]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 316−1, defining interval I = [0,15], and minimum distance d ≥ |{−15,−14,…,15}|+1 = 32 (BCH-bound) [i]
- linear OA(316, 64, F3, 7) (dual of [64, 48, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(316, 82, F3, 7) (dual of [82, 66, 8]-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(3227, 5979, F3, 2, 39) (dual of [(5979, 2), 11731, 40]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3227, 5979, F3, 3, 39) (dual of [(5979, 3), 17710, 40]-NRT-code) | [i] | ||
| 3 | Linear OOA(3227, 5979, F3, 4, 39) (dual of [(5979, 4), 23689, 40]-NRT-code) | [i] | ||
| 4 | Linear OOA(3227, 5979, F3, 5, 39) (dual of [(5979, 5), 29668, 40]-NRT-code) | [i] | ||
| 5 | Digital (188, 227, 5979)-net over F3 | [i] | ||
| 6 | Linear OOA(3227, 1657, F3, 4, 39) (dual of [(1657, 4), 6401, 40]-NRT-code) | [i] | OOA Folding | |