Information on Result #1361894
Linear OOA(395, 9854, F3, 2, 15) (dual of [(9854, 2), 19613, 16]-NRT-code), using OOA 2-folding based on linear OA(395, 19708, F3, 15) (dual of [19708, 19613, 16]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(392, 19704, F3, 15) (dual of [19704, 19612, 16]-code), using
- construction X4 applied to C([0,7]) ⊂ C([0,6]) [i] based on
- linear OA(391, 19684, F3, 15) (dual of [19684, 19593, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 19684 | 318−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- linear OA(373, 19684, F3, 13) (dual of [19684, 19611, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 19684 | 318−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (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
- construction X4 applied to C([0,7]) ⊂ C([0,6]) [i] based on
- linear OA(392, 19705, F3, 12) (dual of [19705, 19613, 13]-code), using Gilbert–Varšamov bound and bm = 392 > Vbs−1(k−1) = 8 895727 183920 215746 695430 323734 252372 012641 [i]
- linear OA(32, 3, F3, 2) (dual of [3, 1, 3]-code or 3-arc in PG(1,3)), using
- dual of repetition code with length 3 [i]
- Reed–Solomon code RS(1,3) [i]
- linear OA(392, 19704, F3, 15) (dual of [19704, 19612, 16]-code), using
Mode: 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(395, 9854, F3, 3, 15) (dual of [(9854, 3), 29467, 16]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(395, 9854, F3, 4, 15) (dual of [(9854, 4), 39321, 16]-NRT-code) | [i] | ||
| 3 | Linear OOA(395, 9854, F3, 5, 15) (dual of [(9854, 5), 49175, 16]-NRT-code) | [i] | ||
| 4 | Digital (80, 95, 9854)-net over F3 | [i] | ||