Information on Result #682121
Linear OA(538, 1953145, F5, 5) (dual of [1953145, 1953107, 6]-code), using construction X applied to C([0,2]) ⊂ C([0,1]) based on
- linear OA(537, 1953126, F5, 5) (dual of [1953126, 1953089, 6]-code), using the expurgated narrow-sense BCH-code C(I) with length 1953126 | 518−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (BCH-bound) [i]
- linear OA(519, 1953126, F5, 3) (dual of [1953126, 1953107, 4]-code or 1953126-cap in PG(18,5)), using the expurgated narrow-sense BCH-code C(I) with length 1953126 | 518−1, defining interval I = [0,1], and minimum distance d ≥ |{−1,0,1}|+1 = 4 (BCH-bound) [i]
- linear OA(51, 19, F5, 1) (dual of [19, 18, 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 OOA(538, 976572, F5, 3, 5) (dual of [(976572, 3), 2929678, 6]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |
| 2 | Linear OOA(538, 976572, F5, 5, 5) (dual of [(976572, 5), 4882822, 6]-NRT-code) | [i] | ||