Information on Result #2485256
Linear OOA(382, 797177, F3, 2, 9) (dual of [(797177, 2), 1594272, 10]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(380, 797176, F3, 2, 9) (dual of [(797176, 2), 1594272, 10]-NRT-code), using
- OOA 2-folding [i] based on linear OA(380, 1594352, F3, 9) (dual of [1594352, 1594272, 10]-code), using
- construction X4 applied to C([0,4]) ⊂ C([0,3]) [i] based on
- linear OA(379, 1594324, F3, 9) (dual of [1594324, 1594245, 10]-code), using the expurgated narrow-sense BCH-code C(I) with length 1594324 | 326−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- linear OA(353, 1594324, F3, 7) (dual of [1594324, 1594271, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 1594324 | 326−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- linear OA(327, 28, F3, 27) (dual of [28, 1, 28]-code or 28-arc in PG(26,3)), using
- dual of repetition code with length 28 [i]
- linear OA(31, 28, F3, 1) (dual of [28, 27, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X4 applied to C([0,4]) ⊂ C([0,3]) [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(383, 797177, F3, 2, 9) (dual of [(797177, 2), 1594271, 10]-NRT-code) | [i] | OOA Duplication | |
| 2 | Linear OOA(382, 797177, F3, 3, 9) (dual of [(797177, 3), 2391449, 10]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(382, 797177, F3, 4, 9) (dual of [(797177, 4), 3188626, 10]-NRT-code) | [i] | ||
| 4 | Linear OOA(382, 797177, F3, 5, 9) (dual of [(797177, 5), 3985803, 10]-NRT-code) | [i] | ||
| 5 | Digital (73, 82, 797177)-net over F3 | [i] | ||