Information on Result #676034
Linear OA(3133, 2214, F3, 27) (dual of [2214, 2081, 28]-code), using construction X applied to Ce(27) ⊂ Ce(22) based on
- linear OA(3127, 2187, F3, 28) (dual of [2187, 2060, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(3106, 2187, F3, 23) (dual of [2187, 2081, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [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(3133, 1659, F3, 2, 27) (dual of [(1659, 2), 3185, 28]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3133, 1659, F3, 3, 27) (dual of [(1659, 3), 4844, 28]-NRT-code) | [i] | ||
| 3 | Linear OOA(3133, 1659, F3, 4, 27) (dual of [(1659, 4), 6503, 28]-NRT-code) | [i] | ||
| 4 | Linear OOA(3133, 1659, F3, 5, 27) (dual of [(1659, 5), 8162, 28]-NRT-code) | [i] | ||
| 5 | Digital (106, 133, 1659)-net over F3 | [i] | ||
| 6 | Linear OOA(3133, 1107, F3, 2, 27) (dual of [(1107, 2), 2081, 28]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(3133, 738, F3, 3, 27) (dual of [(738, 3), 2081, 28]-NRT-code) | [i] | ||
| 8 | Linear OOA(3133, 553, F3, 4, 27) (dual of [(553, 4), 2079, 28]-NRT-code) | [i] | ||
| 9 | Linear OOA(3133, 442, F3, 5, 27) (dual of [(442, 5), 2077, 28]-NRT-code) | [i] | ||