Information on Result #676175
Linear OA(3187, 2207, F3, 39) (dual of [2207, 2020, 40]-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(31, 17, F3, 1) (dual of [17, 16, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- linear OA(31, 3, F3, 1) (dual of [3, 2, 2]-code), using
- Reed–Solomon code RS(2,3) [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(3187, 1800, F3, 2, 39) (dual of [(1800, 2), 3413, 40]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3187, 1800, F3, 3, 39) (dual of [(1800, 3), 5213, 40]-NRT-code) | [i] | ||
| 3 | Linear OOA(3187, 1800, F3, 4, 39) (dual of [(1800, 4), 7013, 40]-NRT-code) | [i] | ||
| 4 | Linear OOA(3187, 1800, F3, 5, 39) (dual of [(1800, 5), 8813, 40]-NRT-code) | [i] | ||
| 5 | Digital (148, 187, 1800)-net over F3 | [i] | ||