Information on Result #2677171
Linear OOA(3152, 177157, F3, 3, 19) (dual of [(177157, 3), 531319, 20]-NRT-code), using 31 times duplication based on linear OOA(3151, 177157, F3, 3, 19) (dual of [(177157, 3), 531320, 20]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3151, 531471, F3, 19) (dual of [531471, 531320, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(3151, 531472, F3, 19) (dual of [531472, 531321, 20]-code), using
- construction X applied to C([0,9]) ⊂ C([0,7]) [i] based on
- linear OA(3145, 531442, F3, 19) (dual of [531442, 531297, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442 | 324−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(3121, 531442, F3, 15) (dual of [531442, 531321, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442 | 324−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- linear OA(36, 30, F3, 3) (dual of [30, 24, 4]-code or 30-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
- construction X applied to C([0,9]) ⊂ C([0,7]) [i] based on
- discarding factors / shortening the dual code based on linear OA(3151, 531472, F3, 19) (dual of [531472, 531321, 20]-code), 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(3152, 176241, F3, 4, 19) (dual of [(176241, 4), 704812, 20]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3152, 176241, F3, 5, 19) (dual of [(176241, 5), 881053, 20]-NRT-code) | [i] | ||
| 3 | Digital (133, 152, 176241)-net over F3 | [i] | ||