Information on Result #736941
Linear OA(3241, 19743, F3, 38) (dual of [19743, 19502, 39]-code), using construction X applied to Ce(37) ⊂ Ce(30) based on
- linear OA(3226, 19683, F3, 38) (dual of [19683, 19457, 39]-code), using an extension Ce(37) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,37], and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(3181, 19683, F3, 31) (dual of [19683, 19502, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(315, 60, F3, 6) (dual of [60, 45, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(315, 85, F3, 6) (dual of [85, 70, 7]-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(3243, 19745, F3, 38) (dual of [19745, 19502, 39]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(3244, 19746, F3, 38) (dual of [19746, 19502, 39]-code) | [i] | ||
| 3 | Linear OA(3245, 19747, F3, 38) (dual of [19747, 19502, 39]-code) | [i] | ||
| 4 | Linear OA(3246, 19748, F3, 38) (dual of [19748, 19502, 39]-code) | [i] | ||
| 5 | Linear OOA(3241, 10792, F3, 2, 38) (dual of [(10792, 2), 21343, 39]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 6 | Linear OOA(3241, 10792, F3, 3, 38) (dual of [(10792, 3), 32135, 39]-NRT-code) | [i] | ||
| 7 | Linear OOA(3241, 10792, F3, 4, 38) (dual of [(10792, 4), 42927, 39]-NRT-code) | [i] | ||
| 8 | Linear OOA(3241, 10792, F3, 5, 38) (dual of [(10792, 5), 53719, 39]-NRT-code) | [i] | ||
| 9 | Digital (203, 241, 10792)-net over F3 | [i] | ||
| 10 | Linear OA(3245, 19748, F3, 38) (dual of [19748, 19503, 39]-code) | [i] | Construction X with Varšamov Bound | |
| 11 | Linear OOA(3241, 9871, F3, 2, 38) (dual of [(9871, 2), 19501, 39]-NRT-code) | [i] | OOA Folding | |
| 12 | Linear OOA(3241, 6581, F3, 3, 38) (dual of [(6581, 3), 19502, 39]-NRT-code) | [i] | ||
| 13 | Linear OOA(3241, 4935, F3, 4, 38) (dual of [(4935, 4), 19499, 39]-NRT-code) | [i] | ||
| 14 | Linear OOA(3241, 3948, F3, 5, 38) (dual of [(3948, 5), 19499, 39]-NRT-code) | [i] | ||