Information on Result #1305105
Linear OA(3204, 2287, F3, 41) (dual of [2287, 2083, 42]-code), using 79 step Varšamov–Edel lengthening with (ri) = (4, 1, 1, 1, 0, 1, 0, 0, 0, 1, 4 times 0, 1, 6 times 0, 1, 8 times 0, 1, 11 times 0, 1, 15 times 0, 1, 20 times 0) based on linear OA(3190, 2194, F3, 41) (dual of [2194, 2004, 42]-code), using
- construction X applied to Ce(40) ⊂ Ce(39) [i] based on
- linear OA(3190, 2187, F3, 41) (dual of [2187, 1997, 42]-code), using an extension Ce(40) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,40], and designed minimum distance d ≥ |I|+1 = 41 [i]
- 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(30, 7, F3, 0) (dual of [7, 7, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(30, s, F3, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
Mode: 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(3204, 2287, F3, 2, 41) (dual of [(2287, 2), 4370, 42]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3204, 2287, F3, 3, 41) (dual of [(2287, 3), 6657, 42]-NRT-code) | [i] | ||
| 3 | Linear OOA(3204, 2287, F3, 4, 41) (dual of [(2287, 4), 8944, 42]-NRT-code) | [i] | ||
| 4 | Linear OOA(3204, 2287, F3, 5, 41) (dual of [(2287, 5), 11231, 42]-NRT-code) | [i] | ||
| 5 | Digital (163, 204, 2287)-net over F3 | [i] | ||
| 6 | Linear OOA(3204, 1143, F3, 2, 41) (dual of [(1143, 2), 2082, 42]-NRT-code) | [i] | OOA Folding | |