Information on Result #2677175
Linear OOA(3164, 531452, F3, 3, 19) (dual of [(531452, 3), 1594192, 20]-NRT-code), using 31 times duplication based on linear OOA(3163, 531452, F3, 3, 19) (dual of [(531452, 3), 1594193, 20]-NRT-code), using
- OOA 3-folding [i] 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
- construction X applied to C([0,9]) ⊂ C([0,7]) [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(3164, 424447, F3, 4, 19) (dual of [(424447, 4), 1697624, 20]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3164, 424447, F3, 5, 19) (dual of [(424447, 5), 2122071, 20]-NRT-code) | [i] | ||
| 3 | Digital (145, 164, 424447)-net over F3 | [i] | ||