Information on Result #675404
Linear OA(3226, 6627, F3, 39) (dual of [6627, 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(317, 65, F3, 7) (dual of [65, 48, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(317, 80, F3, 7) (dual of [80, 63, 8]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 80 = 34−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 8 [i]
- discarding factors / shortening the dual code based on linear OA(317, 80, F3, 7) (dual of [80, 63, 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(3226, 5803, F3, 2, 39) (dual of [(5803, 2), 11380, 40]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3226, 5803, F3, 3, 39) (dual of [(5803, 3), 17183, 40]-NRT-code) | [i] | ||
| 3 | Linear OOA(3226, 5803, F3, 4, 39) (dual of [(5803, 4), 22986, 40]-NRT-code) | [i] | ||
| 4 | Linear OOA(3226, 5803, F3, 5, 39) (dual of [(5803, 5), 28789, 40]-NRT-code) | [i] | ||
| 5 | Digital (187, 226, 5803)-net over F3 | [i] | ||
| 6 | Linear OOA(3226, 2209, F3, 3, 39) (dual of [(2209, 3), 6401, 40]-NRT-code) | [i] | OOA Folding | |