Information on Result #676176
Linear OA(3189, 2208, F3, 40) (dual of [2208, 2019, 41]-code), using construction XX applied to Ce(39) ⊂ Ce(36) ⊂ Ce(34) based on
- linear OA(3183, 2187, F3, 40) (dual of [2187, 2004, 41]-code), using an extension Ce(39) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,39], and designed minimum distance d ≥ |I|+1 = 40 [i]
- linear OA(3169, 2187, F3, 37) (dual of [2187, 2018, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(3162, 2187, F3, 35) (dual of [2187, 2025, 36]-code), using an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(34, 19, F3, 2) (dual of [19, 15, 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
- linear OA(31, 2, F3, 1) (dual of [2, 1, 2]-code), using
- dual of repetition code with length 2 [i]
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(3189, 1688, F3, 2, 40) (dual of [(1688, 2), 3187, 41]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3189, 1688, F3, 3, 40) (dual of [(1688, 3), 4875, 41]-NRT-code) | [i] | ||
| 3 | Linear OOA(3189, 1688, F3, 4, 40) (dual of [(1688, 4), 6563, 41]-NRT-code) | [i] | ||
| 4 | Linear OOA(3189, 1688, F3, 5, 40) (dual of [(1688, 5), 8251, 41]-NRT-code) | [i] | ||
| 5 | Digital (149, 189, 1688)-net over F3 | [i] | ||
| 6 | Linear OOA(3189, 1104, F3, 2, 40) (dual of [(1104, 2), 2019, 41]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(3189, 736, F3, 3, 40) (dual of [(736, 3), 2019, 41]-NRT-code) | [i] | ||
| 8 | Linear OOA(3189, 552, F3, 4, 40) (dual of [(552, 4), 2019, 41]-NRT-code) | [i] | ||