Information on Result #682122
Linear OA(538, 1953146, F5, 5) (dual of [1953146, 1953108, 6]-code), using construction X4 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(519, 20, F5, 19) (dual of [20, 1, 20]-code or 20-arc in PG(18,5)), using
- dual of repetition code with length 20 [i]
- linear OA(51, 20, F5, 1) (dual of [20, 19, 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, 976573, F5, 2, 5) (dual of [(976573, 2), 1953108, 6]-NRT-code) | [i] | OOA Folding | |