Information on Result #682584
Linear OA(574, 15639, F5, 15) (dual of [15639, 15565, 16]-code), using construction X applied to C([0,7]) ⊂ C([0,6]) based on
- linear OA(573, 15626, F5, 15) (dual of [15626, 15553, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 15626 | 512−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- linear OA(561, 15626, F5, 13) (dual of [15626, 15565, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 15626 | 512−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(51, 13, F5, 1) (dual of [13, 12, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(51, s, F5, 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(575, 15640, F5, 15) (dual of [15640, 15565, 16]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(574, 11913, F5, 2, 15) (dual of [(11913, 2), 23752, 16]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(574, 11913, F5, 3, 15) (dual of [(11913, 3), 35665, 16]-NRT-code) | [i] | ||
| 4 | Digital (59, 74, 11913)-net over F5 | [i] | ||
| 5 | Linear OOA(574, 7819, F5, 2, 15) (dual of [(7819, 2), 15564, 16]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(574, 5213, F5, 3, 15) (dual of [(5213, 3), 15565, 16]-NRT-code) | [i] | ||
| 7 | Linear OOA(574, 2234, F5, 15, 15) (dual of [(2234, 15), 33436, 16]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |