Information on Result #682415
Linear OA(590, 78159, F5, 15) (dual of [78159, 78069, 16]-code), using construction X applied to C([0,7]) ⊂ C([0,5]) based on
- linear OA(585, 78126, F5, 15) (dual of [78126, 78041, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 78126 | 514−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- linear OA(557, 78126, F5, 11) (dual of [78126, 78069, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 78126 | 514−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- linear OA(55, 33, F5, 3) (dual of [33, 28, 4]-code or 33-cap in PG(4,5)), using
- discarding factors / shortening the dual code based on linear OA(55, 42, F5, 3) (dual of [42, 37, 4]-code or 42-cap in PG(4,5)), 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(591, 78160, F5, 15) (dual of [78160, 78069, 16]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(592, 78161, F5, 15) (dual of [78161, 78069, 16]-code) | [i] | ||
| 3 | Linear OA(593, 78162, F5, 15) (dual of [78162, 78069, 16]-code) | [i] | ||
| 4 | Linear OOA(590, 78159, F5, 2, 15) (dual of [(78159, 2), 156228, 16]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 5 | Linear OOA(590, 78159, F5, 3, 15) (dual of [(78159, 3), 234387, 16]-NRT-code) | [i] | ||
| 6 | Digital (75, 90, 78159)-net over F5 | [i] | ||
| 7 | Linear OA(591, 78161, F5, 15) (dual of [78161, 78070, 16]-code) | [i] | Construction X with Varšamov Bound | |
| 8 | Linear OA(592, 78163, F5, 15) (dual of [78163, 78071, 16]-code) | [i] | ||
| 9 | Linear OA(593, 78165, F5, 15) (dual of [78165, 78072, 16]-code) | [i] | ||
| 10 | Linear OOA(590, 39079, F5, 2, 15) (dual of [(39079, 2), 78068, 16]-NRT-code) | [i] | OOA Folding | |
| 11 | Linear OOA(590, 26053, F5, 3, 15) (dual of [(26053, 3), 78069, 16]-NRT-code) | [i] | ||
| 12 | Linear OOA(590, 11165, F5, 15, 15) (dual of [(11165, 15), 167385, 16]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |