Information on Result #812945
Linear OOA(3111, 797184, F3, 2, 12) (dual of [(797184, 2), 1594257, 13]-NRT-code), using OOA 2-folding based on linear OA(3111, 1594368, F3, 12) (dual of [1594368, 1594257, 13]-code), using
- construction X applied to Ce(12) ⊂ Ce(7) [i] based on
- linear OA(3105, 1594323, F3, 13) (dual of [1594323, 1594218, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(366, 1594323, F3, 8) (dual of [1594323, 1594257, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(36, 45, F3, 3) (dual of [45, 39, 4]-code or 45-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(3111, 797184, F3, 3, 12) (dual of [(797184, 3), 2391441, 13]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3111, 797184, F3, 4, 12) (dual of [(797184, 4), 3188625, 13]-NRT-code) | [i] | ||
| 3 | Linear OOA(3111, 797184, F3, 5, 12) (dual of [(797184, 5), 3985809, 13]-NRT-code) | [i] | ||
| 4 | Digital (99, 111, 797184)-net over F3 | [i] | ||