Information on Result #1060574
Linear OOA(3163, 398589, F3, 4, 19) (dual of [(398589, 4), 1594193, 20]-NRT-code), using OOA 4-folding based on linear OA(3163, 1594356, F3, 19) (dual of [1594356, 1594193, 20]-code), using
- construction X applied to C([0,9]) ⊂ C([0,7]) [i] based on
- linear OA(3157, 1594324, F3, 19) (dual of [1594324, 1594167, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 1594324 | 326−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(3131, 1594324, F3, 15) (dual of [1594324, 1594193, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 1594324 | 326−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- linear OA(36, 32, F3, 3) (dual of [32, 26, 4]-code or 32-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(3164, 398589, F3, 4, 19) (dual of [(398589, 4), 1594192, 20]-NRT-code) | [i] | OOA Duplication | |
| 2 | Linear OOA(3162, 398588, F3, 4, 18) (dual of [(398588, 4), 1594190, 19]-NRT-code) | [i] | Truncation for OOAs | |
| 3 | Linear OOA(3163, 398589, F3, 5, 19) (dual of [(398589, 5), 1992782, 20]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Digital (144, 163, 398589)-net over F3 | [i] | ||