Information on Result #676002
Linear OA(3231, 2214, F3, 48) (dual of [2214, 1983, 49]-code), using construction X applied to Ce(48) ⊂ Ce(43) based on
- linear OA(3225, 2187, F3, 49) (dual of [2187, 1962, 50]-code), using an extension Ce(48) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,48], and designed minimum distance d ≥ |I|+1 = 49 [i]
- linear OA(3204, 2187, F3, 44) (dual of [2187, 1983, 45]-code), using an extension Ce(43) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,43], and designed minimum distance d ≥ |I|+1 = 44 [i]
- linear OA(36, 27, F3, 3) (dual of [27, 21, 4]-code or 27-cap in PG(5,3)), using
- discarding factors / shortening the dual code based on linear OA(36, 48, F3, 3) (dual of [48, 42, 4]-code or 48-cap in PG(5,3)), 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 OOA(3231, 2144, F3, 2, 48) (dual of [(2144, 2), 4057, 49]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3231, 2144, F3, 3, 48) (dual of [(2144, 3), 6201, 49]-NRT-code) | [i] | ||
| 3 | Linear OOA(3231, 2144, F3, 4, 48) (dual of [(2144, 4), 8345, 49]-NRT-code) | [i] | ||
| 4 | Linear OOA(3231, 2144, F3, 5, 48) (dual of [(2144, 5), 10489, 49]-NRT-code) | [i] | ||
| 5 | Digital (183, 231, 2144)-net over F3 | [i] | ||
| 6 | Linear OOA(3231, 1107, F3, 2, 48) (dual of [(1107, 2), 1983, 49]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(3231, 738, F3, 3, 48) (dual of [(738, 3), 1983, 49]-NRT-code) | [i] | ||
| 8 | Linear OOA(3231, 553, F3, 4, 48) (dual of [(553, 4), 1981, 49]-NRT-code) | [i] | ||
| 9 | Linear OOA(3231, 442, F3, 5, 48) (dual of [(442, 5), 1979, 49]-NRT-code) | [i] | ||