Information on Result #815771
Linear OOA(3218, 9851, F3, 2, 36) (dual of [(9851, 2), 19484, 37]-NRT-code), using OOA 2-folding based on linear OA(3218, 19702, F3, 36) (dual of [19702, 19484, 37]-code), using
- construction X applied to Ce(36) ⊂ Ce(33) [i] based on
- linear OA(3217, 19683, F3, 37) (dual of [19683, 19466, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(3199, 19683, F3, 34) (dual of [19683, 19484, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(31, 19, F3, 1) (dual of [19, 18, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, 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(3220, 9852, F3, 2, 36) (dual of [(9852, 2), 19484, 37]-NRT-code) | [i] | NRT-Code Embedding in Larger Space | |
| 2 | Linear OOA(3219, 9851, F3, 2, 36) (dual of [(9851, 2), 19483, 37]-NRT-code) | [i] | OOA Duplication | |
| 3 | Linear OOA(3218, 8704, F3, 3, 36) (dual of [(8704, 3), 25894, 37]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(3218, 8704, F3, 4, 36) (dual of [(8704, 4), 34598, 37]-NRT-code) | [i] | ||
| 5 | Linear OOA(3218, 8704, F3, 5, 36) (dual of [(8704, 5), 43302, 37]-NRT-code) | [i] | ||
| 6 | Digital (182, 218, 8704)-net over F3 | [i] | ||