Information on Result #1831513
OOA(2174, 4196355, S2, 2, 13), using (u, u+v)-construction based on
- OOA(235, 2054, S2, 2, 6), using
- OOA 2-folding [i] based on OA(235, 4108, S2, 6), using
- 1 times truncation [i] based on OA(236, 4109, S2, 7), using
- construction X4 applied to K(12) ⊂ DG(12,5) [i] based on
- OA(235, 4096, S2, 7), using Delsarte–Goethals OA DG(12,5) [i]
- OA(224, 4096, S2, 5), using Kerdock OA K(12) [i]
- linear OA(212, 13, F2, 11) (dual of [13, 1, 12]-code), using
- strength reduction [i] based on linear OA(212, 13, F2, 12) (dual of [13, 1, 13]-code or 13-arc in PG(11,2)), using
- dual of repetition code with length 13 [i]
- strength reduction [i] based on linear OA(212, 13, F2, 12) (dual of [13, 1, 13]-code or 13-arc in PG(11,2)), using
- linear OA(21, 13, F2, 1) (dual of [13, 12, 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(12) ⊂ DG(12,5) [i] based on
- 1 times truncation [i] based on OA(236, 4109, S2, 7), using
- OOA 2-folding [i] based on OA(235, 4108, 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(2174, 4196355, S2, 2, 12) | [i] | Strength Reduction for OOAs | |
| 2 | OOA(2175, 4196355, S2, 2, 13) | [i] | OOA Duplication | |