Information on Result #675455
Linear OA(3221, 6581, F3, 41) (dual of [6581, 6360, 42]-code), using construction X applied to Ce(40) ⊂ Ce(37) based on
- linear OA(3217, 6561, F3, 41) (dual of [6561, 6344, 42]-code), using an extension Ce(40) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,40], and designed minimum distance d ≥ |I|+1 = 41 [i]
- linear OA(3201, 6561, F3, 38) (dual of [6561, 6360, 39]-code), using an extension Ce(37) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,37], and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(34, 20, F3, 2) (dual of [20, 16, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(34, 40, F3, 2) (dual of [40, 36, 3]-code), using
- Hamming code H(4,3) [i]
- discarding factors / shortening the dual code based on linear OA(34, 40, F3, 2) (dual of [40, 36, 3]-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(3221, 3746, F3, 2, 41) (dual of [(3746, 2), 7271, 42]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3221, 3746, F3, 3, 41) (dual of [(3746, 3), 11017, 42]-NRT-code) | [i] | ||
| 3 | Linear OOA(3221, 3746, F3, 4, 41) (dual of [(3746, 4), 14763, 42]-NRT-code) | [i] | ||
| 4 | Linear OOA(3221, 3746, F3, 5, 41) (dual of [(3746, 5), 18509, 42]-NRT-code) | [i] | ||
| 5 | Digital (180, 221, 3746)-net over F3 | [i] | ||
| 6 | Linear OOA(3221, 3290, F3, 2, 41) (dual of [(3290, 2), 6359, 42]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(3221, 2193, F3, 3, 41) (dual of [(2193, 3), 6358, 42]-NRT-code) | [i] | ||
| 8 | Linear OOA(3221, 1645, F3, 4, 41) (dual of [(1645, 4), 6359, 42]-NRT-code) | [i] | ||
| 9 | Linear OOA(3221, 1316, F3, 5, 41) (dual of [(1316, 5), 6359, 42]-NRT-code) | [i] | ||