Information on Result #1831514
OOA(2180, 4202500, S2, 2, 13), using (u, u+v)-construction based on
- OOA(241, 8199, S2, 2, 6), using
- OOA 2-folding [i] based on OA(241, 16398, S2, 6), using
- 1 times truncation [i] based on OA(242, 16399, S2, 7), using
- construction X4 applied to K(14) ⊂ DG(14,6) [i] based on
- OA(241, 16384, S2, 7), using Delsarte–Goethals OA DG(14,6) [i]
- OA(228, 16384, S2, 5), using Kerdock OA K(14) [i]
- linear OA(214, 15, F2, 13) (dual of [15, 1, 14]-code), using
- strength reduction [i] based on linear OA(214, 15, F2, 14) (dual of [15, 1, 15]-code or 15-arc in PG(13,2)), using
- dual of repetition code with length 15 [i]
- strength reduction [i] based on linear OA(214, 15, F2, 14) (dual of [15, 1, 15]-code or 15-arc in PG(13,2)), using
- linear OA(21, 15, F2, 1) (dual of [15, 14, 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(14) ⊂ DG(14,6) [i] based on
- 1 times truncation [i] based on OA(242, 16399, S2, 7), using
- OOA 2-folding [i] based on OA(241, 16398, 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(2180, 4202500, S2, 2, 12) | [i] | Strength Reduction for OOAs | |
| 2 | OOA(2181, 4202500, S2, 2, 13) | [i] | OOA Duplication | |