Information on Result #675384
Linear OA(3169, 6602, F3, 30) (dual of [6602, 6433, 31]-code), using construction X applied to C([0,15]) ⊂ C([0,12]) based on
- 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(3129, 6562, F3, 25) (dual of [6562, 6433, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 316−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (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 OA(3170, 6603, F3, 30) (dual of [6603, 6433, 31]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(3174, 6607, F3, 30) (dual of [6607, 6433, 31]-code) | [i] | ||
| 3 | Linear OOA(3169, 4092, F3, 2, 30) (dual of [(4092, 2), 8015, 31]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(3169, 4092, F3, 3, 30) (dual of [(4092, 3), 12107, 31]-NRT-code) | [i] | ||
| 5 | Linear OOA(3169, 4092, F3, 4, 30) (dual of [(4092, 4), 16199, 31]-NRT-code) | [i] | ||
| 6 | Linear OOA(3169, 4092, F3, 5, 30) (dual of [(4092, 5), 20291, 31]-NRT-code) | [i] | ||
| 7 | Digital (139, 169, 4092)-net over F3 | [i] | ||
| 8 | Linear OA(3172, 6606, F3, 30) (dual of [6606, 6434, 31]-code) | [i] | Construction X with Varšamov Bound | |
| 9 | Linear OA(3173, 6608, F3, 30) (dual of [6608, 6435, 31]-code) | [i] | ||
| 10 | Linear OOA(3169, 3301, F3, 2, 30) (dual of [(3301, 2), 6433, 31]-NRT-code) | [i] | OOA Folding | |
| 11 | Linear OOA(3169, 2200, F3, 3, 30) (dual of [(2200, 3), 6431, 31]-NRT-code) | [i] | ||
| 12 | Linear OOA(3169, 1650, F3, 4, 30) (dual of [(1650, 4), 6431, 31]-NRT-code) | [i] | ||
| 13 | Linear OOA(3169, 1320, F3, 5, 30) (dual of [(1320, 5), 6431, 31]-NRT-code) | [i] | ||