Information on Result #815150
Linear OOA(3197, 9872, F3, 2, 31) (dual of [(9872, 2), 19547, 32]-NRT-code), using OOA 2-folding based on linear OA(3197, 19744, F3, 31) (dual of [19744, 19547, 32]-code), using
- construction X applied to Ce(30) ⊂ Ce(22) [i] based on
- 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(3136, 19683, F3, 23) (dual of [19683, 19547, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(316, 61, F3, 7) (dual of [61, 45, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(316, 82, F3, 7) (dual of [82, 66, 8]-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(3199, 9873, F3, 2, 31) (dual of [(9873, 2), 19547, 32]-NRT-code) | [i] | NRT-Code Embedding in Larger Space | |
| 2 | Linear OOA(3198, 9872, F3, 2, 31) (dual of [(9872, 2), 19546, 32]-NRT-code) | [i] | OOA Duplication | |
| 3 | Linear OOA(3197, 9872, F3, 3, 31) (dual of [(9872, 3), 29419, 32]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(3197, 9872, F3, 4, 31) (dual of [(9872, 4), 39291, 32]-NRT-code) | [i] | ||
| 5 | Linear OOA(3197, 9872, F3, 5, 31) (dual of [(9872, 5), 49163, 32]-NRT-code) | [i] | ||
| 6 | Digital (166, 197, 9872)-net over F3 | [i] | ||