Information on Result #2263969
Linear OA(357, 19705, F3, 9) (dual of [19705, 19648, 10]-code), using 1 times code embedding in larger space based on linear OA(356, 19704, F3, 9) (dual of [19704, 19648, 10]-code), using
- construction X4 applied to C([0,4]) ⊂ C([0,3]) [i] based on
- linear OA(355, 19684, F3, 9) (dual of [19684, 19629, 10]-code), using the expurgated narrow-sense BCH-code C(I) with length 19684 | 318−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- linear OA(337, 19684, F3, 7) (dual of [19684, 19647, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 19684 | 318−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- linear OA(319, 20, F3, 19) (dual of [20, 1, 20]-code or 20-arc in PG(18,3)), using
- dual of repetition code with length 20 [i]
- linear OA(31, 20, F3, 1) (dual of [20, 19, 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
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(357, 11082, F3, 2, 9) (dual of [(11082, 2), 22107, 10]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(357, 11082, F3, 3, 9) (dual of [(11082, 3), 33189, 10]-NRT-code) | [i] | ||
| 3 | Linear OOA(357, 11082, F3, 4, 9) (dual of [(11082, 4), 44271, 10]-NRT-code) | [i] | ||
| 4 | Linear OOA(357, 11082, F3, 5, 9) (dual of [(11082, 5), 55353, 10]-NRT-code) | [i] | ||
| 5 | Digital (48, 57, 11082)-net over F3 | [i] | ||
| 6 | Linear OOA(357, 4926, F3, 5, 9) (dual of [(4926, 5), 24573, 10]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |
| 7 | Linear OOA(357, 4926, F3, 9, 9) (dual of [(4926, 9), 44277, 10]-NRT-code) | [i] | ||