Information on Result #736975
Linear OA(3225, 6626, F3, 39) (dual of [6626, 6401, 40]-code), using construction X applied to C([0,19]) ⊂ C([0,15]) 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 OA(3227, 6628, F3, 39) (dual of [6628, 6401, 40]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(3228, 6629, F3, 39) (dual of [6629, 6401, 40]-code) | [i] | ||
| 3 | Linear OA(3229, 6630, F3, 39) (dual of [6630, 6401, 40]-code) | [i] | ||
| 4 | Linear OA(3230, 6631, F3, 39) (dual of [6631, 6401, 40]-code) | [i] | ||
| 5 | Linear OA(3231, 6632, F3, 39) (dual of [6632, 6401, 40]-code) | [i] | ||
| 6 | Linear OA(3232, 6633, F3, 39) (dual of [6633, 6401, 40]-code) | [i] | ||
| 7 | Linear OOA(3225, 5632, F3, 2, 39) (dual of [(5632, 2), 11039, 40]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 8 | Linear OOA(3225, 5632, F3, 3, 39) (dual of [(5632, 3), 16671, 40]-NRT-code) | [i] | ||
| 9 | Linear OOA(3225, 5632, F3, 4, 39) (dual of [(5632, 4), 22303, 40]-NRT-code) | [i] | ||
| 10 | Linear OOA(3225, 5632, F3, 5, 39) (dual of [(5632, 5), 27935, 40]-NRT-code) | [i] | ||
| 11 | Digital (186, 225, 5632)-net over F3 | [i] | ||
| 12 | Linear OA(3227, 6629, F3, 39) (dual of [6629, 6402, 40]-code) | [i] | Construction X with Varšamov Bound | |
| 13 | Linear OA(3228, 6631, F3, 39) (dual of [6631, 6403, 40]-code) | [i] | ||
| 14 | Linear OA(3229, 6633, F3, 39) (dual of [6633, 6404, 40]-code) | [i] | ||
| 15 | Linear OA(3230, 6635, F3, 39) (dual of [6635, 6405, 40]-code) | [i] | ||
| 16 | Linear OA(3231, 6637, F3, 39) (dual of [6637, 6406, 40]-code) | [i] | ||
| 17 | Linear OA(3232, 6639, F3, 39) (dual of [6639, 6407, 40]-code) | [i] | ||
| 18 | Linear OOA(3225, 3313, F3, 2, 39) (dual of [(3313, 2), 6401, 40]-NRT-code) | [i] | OOA Folding | |
| 19 | Linear OOA(3225, 2208, F3, 3, 39) (dual of [(2208, 3), 6399, 40]-NRT-code) | [i] | ||
| 20 | Linear OOA(3225, 1656, F3, 4, 39) (dual of [(1656, 4), 6399, 40]-NRT-code) | [i] | ||
| 21 | Linear OOA(3225, 1325, F3, 5, 39) (dual of [(1325, 5), 6400, 40]-NRT-code) | [i] | ||