Information on Result #737089
Linear OA(3185, 2238, F3, 37) (dual of [2238, 2053, 38]-code), using construction X applied to Ce(36) ⊂ Ce(28) based on
- 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(3134, 2187, F3, 29) (dual of [2187, 2053, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(316, 51, F3, 7) (dual of [51, 35, 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 OA(3187, 2240, F3, 37) (dual of [2240, 2053, 38]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(3188, 2241, F3, 37) (dual of [2241, 2053, 38]-code) | [i] | ||
| 3 | Linear OA(3189, 2242, F3, 37) (dual of [2242, 2053, 38]-code) | [i] | ||
| 4 | Linear OA(3184, 2237, F3, 36) (dual of [2237, 2053, 37]-code) | [i] | Truncation | |
| 5 | Linear OOA(3185, 2209, F3, 2, 37) (dual of [(2209, 2), 4233, 38]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 6 | Linear OOA(3185, 2209, F3, 3, 37) (dual of [(2209, 3), 6442, 38]-NRT-code) | [i] | ||
| 7 | Linear OOA(3185, 2209, F3, 4, 37) (dual of [(2209, 4), 8651, 38]-NRT-code) | [i] | ||
| 8 | Linear OOA(3185, 2209, F3, 5, 37) (dual of [(2209, 5), 10860, 38]-NRT-code) | [i] | ||
| 9 | Digital (148, 185, 2209)-net over F3 | [i] | ||
| 10 | Linear OA(3186, 2240, F3, 37) (dual of [2240, 2054, 38]-code) | [i] | Construction X with Varšamov Bound | |
| 11 | Linear OA(3187, 2242, F3, 37) (dual of [2242, 2055, 38]-code) | [i] | ||
| 12 | Linear OA(3188, 2244, F3, 37) (dual of [2244, 2056, 38]-code) | [i] | ||
| 13 | Linear OOA(3185, 1119, F3, 2, 37) (dual of [(1119, 2), 2053, 38]-NRT-code) | [i] | OOA Folding | |
| 14 | Linear OOA(3185, 746, F3, 3, 37) (dual of [(746, 3), 2053, 38]-NRT-code) | [i] | ||
| 15 | Linear OOA(3185, 559, F3, 4, 37) (dual of [(559, 4), 2051, 38]-NRT-code) | [i] | ||
| 16 | Linear OOA(3185, 447, F3, 5, 37) (dual of [(447, 5), 2050, 38]-NRT-code) | [i] | ||