Information on Result #676007
Linear OA(3217, 2214, F3, 45) (dual of [2214, 1997, 46]-code), using construction X applied to Ce(45) ⊂ Ce(40) based on
- linear OA(3211, 2187, F3, 46) (dual of [2187, 1976, 47]-code), using an extension Ce(45) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,45], and designed minimum distance d ≥ |I|+1 = 46 [i]
- 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(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(3217, 2065, F3, 2, 45) (dual of [(2065, 2), 3913, 46]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3217, 2065, F3, 3, 45) (dual of [(2065, 3), 5978, 46]-NRT-code) | [i] | ||
| 3 | Linear OOA(3217, 2065, F3, 4, 45) (dual of [(2065, 4), 8043, 46]-NRT-code) | [i] | ||
| 4 | Linear OOA(3217, 2065, F3, 5, 45) (dual of [(2065, 5), 10108, 46]-NRT-code) | [i] | ||
| 5 | Digital (172, 217, 2065)-net over F3 | [i] | ||
| 6 | Linear OOA(3217, 1107, F3, 2, 45) (dual of [(1107, 2), 1997, 46]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(3217, 738, F3, 3, 45) (dual of [(738, 3), 1997, 46]-NRT-code) | [i] | ||
| 8 | Linear OOA(3217, 553, F3, 4, 45) (dual of [(553, 4), 1995, 46]-NRT-code) | [i] | ||
| 9 | Linear OOA(3217, 442, F3, 5, 45) (dual of [(442, 5), 1993, 46]-NRT-code) | [i] | ||