Information on Result #1821604
OA(237, 262163, S2, 5), using construction X4 applied to RM(1,18) ⊂ K(18) based on
- OA(236, 262144, S2, 5), using Kerdock OA K(18) [i]
- linear OA(219, 262144, F2, 3) (dual of [262144, 262125, 4]-code or 262144-cap in PG(18,2)), using Reed–Muller code RM(1,18) [i]
- linear OA(218, 19, F2, 17) (dual of [19, 1, 18]-code), using
- strength reduction [i] based on linear OA(218, 19, F2, 18) (dual of [19, 1, 19]-code or 19-arc in PG(17,2)), using
- dual of repetition code with length 19 [i]
- strength reduction [i] based on linear OA(218, 19, F2, 18) (dual of [19, 1, 19]-code or 19-arc in PG(17,2)), using
- linear OA(21, 19, F2, 1) (dual of [19, 18, 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
Mode: Constructive.
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 | OA(236, 262162, S2, 4) | [i] | Truncation | |
| 2 | OOA(237, 131081, S2, 3, 5) | [i] | OOA Folding and Stacking with Additional Row | |
| 3 | OOA(237, 131081, S2, 4, 5) | [i] | ||
| 4 | OOA(237, 131081, S2, 5, 5) | [i] | ||