Information on Result #1305108
Linear OA(3207, 2389, F3, 41) (dual of [2389, 2182, 42]-code), using 178 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, 1, 26 times 0, 1, 32 times 0, 1, 38 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(3207, 2389, F3, 2, 41) (dual of [(2389, 2), 4571, 42]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3207, 2389, F3, 3, 41) (dual of [(2389, 3), 6960, 42]-NRT-code) | [i] | ||
| 3 | Linear OOA(3207, 2389, F3, 4, 41) (dual of [(2389, 4), 9349, 42]-NRT-code) | [i] | ||
| 4 | Linear OOA(3207, 2389, F3, 5, 41) (dual of [(2389, 5), 11738, 42]-NRT-code) | [i] | ||
| 5 | Digital (166, 207, 2389)-net over F3 | [i] | ||
| 6 | Linear OOA(3207, 1194, F3, 2, 41) (dual of [(1194, 2), 2181, 42]-NRT-code) | [i] | OOA Folding | |