Information on Result #675053
Linear OA(3190, 19729, F3, 30) (dual of [19729, 19539, 31]-code), using construction X applied to C([0,15]) ⊂ C([0,12]) based on
- linear OA(3181, 19684, F3, 31) (dual of [19684, 19503, 32]-code), using the expurgated narrow-sense BCH-code C(I) with length 19684 | 318−1, defining interval I = [0,15], and minimum distance d ≥ |{−15,−14,…,15}|+1 = 32 (BCH-bound) [i]
- linear OA(3145, 19684, F3, 25) (dual of [19684, 19539, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 19684 | 318−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(39, 45, F3, 4) (dual of [45, 36, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(39, 80, F3, 4) (dual of [80, 71, 5]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 80 = 34−1, defining interval I = [0,2], and designed minimum distance d ≥ |I|+1 = 5 [i]
- discarding factors / shortening the dual code based on linear OA(39, 80, F3, 4) (dual of [80, 71, 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(3194, 19733, F3, 30) (dual of [19733, 19539, 31]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(3194, 19734, F3, 30) (dual of [19734, 19540, 31]-code) | [i] | Construction X with Varšamov Bound | |
| 3 | Linear OOA(3190, 9864, F3, 2, 30) (dual of [(9864, 2), 19538, 31]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(3190, 6576, F3, 3, 30) (dual of [(6576, 3), 19538, 31]-NRT-code) | [i] | ||
| 5 | Linear OOA(3190, 4932, F3, 4, 30) (dual of [(4932, 4), 19538, 31]-NRT-code) | [i] | ||