Information on Result #812950
Linear OOA(3119, 2391508, F3, 2, 12) (dual of [(2391508, 2), 4782897, 13]-NRT-code), using OOA 2-folding based on linear OA(3119, 4783016, F3, 12) (dual of [4783016, 4782897, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(3119, 4783017, F3, 12) (dual of [4783017, 4782898, 13]-code), using
- construction X applied to Ce(12) ⊂ Ce(7) [i] based on
- linear OA(3113, 4782969, F3, 13) (dual of [4782969, 4782856, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(371, 4782969, F3, 8) (dual of [4782969, 4782898, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(36, 48, F3, 3) (dual of [48, 42, 4]-code or 48-cap in PG(5,3)), using
- construction X applied to Ce(12) ⊂ Ce(7) [i] based on
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(3119, 2391508, F3, 3, 12) (dual of [(2391508, 3), 7174405, 13]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3119, 2391508, F3, 4, 12) (dual of [(2391508, 4), 9565913, 13]-NRT-code) | [i] | ||
| 3 | Linear OOA(3119, 2391508, F3, 5, 12) (dual of [(2391508, 5), 11957421, 13]-NRT-code) | [i] | ||
| 4 | Digital (107, 119, 2391508)-net over F3 | [i] | ||