Information on Result #675016
Linear OA(392, 19704, F3, 15) (dual of [19704, 19612, 16]-code), using construction X4 applied to C([0,7]) ⊂ C([0,6]) 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
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 OA(393, 19705, F3, 15) (dual of [19705, 19612, 16]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(394, 19706, F3, 15) (dual of [19706, 19612, 16]-code) | [i] | ||
| 3 | Linear OA(395, 19707, F3, 15) (dual of [19707, 19612, 16]-code) | [i] | ||
| 4 | Linear OA(395, 19708, F3, 15) (dual of [19708, 19613, 16]-code) | [i] | Construction X with Varšamov Bound | |
| 5 | Linear OA(396, 19710, F3, 15) (dual of [19710, 19614, 16]-code) | [i] | ||
| 6 | Linear OOA(392, 9852, F3, 2, 15) (dual of [(9852, 2), 19612, 16]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(392, 6568, F3, 3, 15) (dual of [(6568, 3), 19612, 16]-NRT-code) | [i] | ||
| 8 | Linear OOA(392, 4926, F3, 4, 15) (dual of [(4926, 4), 19612, 16]-NRT-code) | [i] | ||