Information on Result #1831517
OOA(2198, 4718599, S2, 2, 13), using (u, u+v)-construction based on
- OOA(259, 524298, S2, 2, 6), using
- OOA 2-folding [i] based on OA(259, 1048596, S2, 6), using
- 1 times truncation [i] based on OA(260, 1048597, S2, 7), using
- construction X4 applied to K(20) ⊂ DG(20,9) [i] based on
- OA(259, 1048576, S2, 7), using Delsarte–Goethals OA DG(20,9) [i]
- OA(240, 1048576, S2, 5), using Kerdock OA K(20) [i]
- linear OA(220, 21, F2, 19) (dual of [21, 1, 20]-code), using
- strength reduction [i] based on linear OA(220, 21, F2, 20) (dual of [21, 1, 21]-code or 21-arc in PG(19,2)), using
- dual of repetition code with length 21 [i]
- strength reduction [i] based on linear OA(220, 21, F2, 20) (dual of [21, 1, 21]-code or 21-arc in PG(19,2)), using
- linear OA(21, 21, F2, 1) (dual of [21, 20, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(21, s, F2, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X4 applied to K(20) ⊂ DG(20,9) [i] based on
- 1 times truncation [i] based on OA(260, 1048597, S2, 7), using
- OOA 2-folding [i] based on OA(259, 1048596, S2, 6), using
- linear OOA(2139, 4194301, F2, 2, 13) (dual of [(4194301, 2), 8388463, 14]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2139, 8388602, F2, 13) (dual of [8388602, 8388463, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(2139, large, F2, 13) (dual of [large, large−139, 14]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 8388609 | 246−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(2139, large, F2, 13) (dual of [large, large−139, 14]-code), using
- OOA 2-folding [i] based on linear OA(2139, 8388602, F2, 13) (dual of [8388602, 8388463, 14]-code), using
Mode: Constructive.
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m and t.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | OOA(2198, 4718599, S2, 2, 12) | [i] | Strength Reduction for OOAs | |
| 2 | OOA(2199, 4718599, S2, 2, 13) | [i] | OOA Duplication | |