Information on Result #954900
Linear OOA(3247, 19692, F3, 3, 37) (dual of [(19692, 3), 58829, 38]-NRT-code), using OOA 3-folding based on linear OA(3247, 59076, F3, 37) (dual of [59076, 58829, 38]-code), using
- construction X applied to C([0,18]) ⊂ C([0,16]) [i] based on
- linear OA(3241, 59050, F3, 37) (dual of [59050, 58809, 38]-code), using the expurgated narrow-sense BCH-code C(I) with length 59050 | 320−1, defining interval I = [0,18], and minimum distance d ≥ |{−18,−17,…,18}|+1 = 38 (BCH-bound) [i]
- linear OA(3221, 59050, F3, 33) (dual of [59050, 58829, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 59050 | 320−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
- linear OA(36, 26, F3, 3) (dual of [26, 20, 4]-code or 26-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(3248, 19692, F3, 3, 37) (dual of [(19692, 3), 58828, 38]-NRT-code) | [i] | OOA Duplication | |
2 | Linear OOA(3247, 19692, F3, 4, 37) (dual of [(19692, 4), 78521, 38]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
3 | Linear OOA(3247, 19692, F3, 5, 37) (dual of [(19692, 5), 98213, 38]-NRT-code) | [i] | ||
4 | Digital (210, 247, 19692)-net over F3 | [i] |