Information on Result #2263965
Linear OA(345, 2205, F3, 9) (dual of [2205, 2160, 10]-code), using 1 times code embedding in larger space based on linear OA(344, 2204, F3, 9) (dual of [2204, 2160, 10]-code), using
- construction X4 applied to C([0,4]) ⊂ C([0,3]) [i] based on
- linear OA(343, 2188, F3, 9) (dual of [2188, 2145, 10]-code), using the expurgated narrow-sense BCH-code C(I) with length 2188 | 314−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- linear OA(329, 2188, F3, 7) (dual of [2188, 2159, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 2188 | 314−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- linear OA(315, 16, F3, 15) (dual of [16, 1, 16]-code or 16-arc in PG(14,3)), using
- dual of repetition code with length 16 [i]
- linear OA(31, 16, F3, 1) (dual of [16, 15, 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(345, 1680, F3, 2, 9) (dual of [(1680, 2), 3315, 10]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(345, 1680, F3, 3, 9) (dual of [(1680, 3), 4995, 10]-NRT-code) | [i] | ||
| 3 | Linear OOA(345, 1680, F3, 4, 9) (dual of [(1680, 4), 6675, 10]-NRT-code) | [i] | ||
| 4 | Linear OOA(345, 1680, F3, 5, 9) (dual of [(1680, 5), 8355, 10]-NRT-code) | [i] | ||
| 5 | Digital (36, 45, 1680)-net over F3 | [i] | ||
| 6 | Linear OOA(345, 735, F3, 3, 9) (dual of [(735, 3), 2160, 10]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(345, 551, F3, 5, 9) (dual of [(551, 5), 2710, 10]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |
| 8 | Linear OOA(345, 551, F3, 9, 9) (dual of [(551, 9), 4914, 10]-NRT-code) | [i] | ||