Information on Result #1670905
Linear OOA(2241, 2056, F2, 6, 37) (dual of [(2056, 6), 12095, 38]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(2241, 2056, F2, 4, 37) (dual of [(2056, 4), 7983, 38]-NRT-code), using
- OOA 4-folding [i] based on linear OA(2241, 8224, F2, 37) (dual of [8224, 7983, 38]-code), using
- discarding factors / shortening the dual code based on linear OA(2241, 8225, F2, 37) (dual of [8225, 7984, 38]-code), using
- construction X applied to C([0,18]) ⊂ C([0,16]) [i] based on
- linear OA(2235, 8193, F2, 37) (dual of [8193, 7958, 38]-code), using the expurgated narrow-sense BCH-code C(I) with length 8193 | 226−1, defining interval I = [0,18], and minimum distance d ≥ |{−18,−17,…,18}|+1 = 38 (BCH-bound) [i]
- linear OA(2209, 8193, F2, 33) (dual of [8193, 7984, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 8193 | 226−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
- linear OA(26, 32, F2, 3) (dual of [32, 26, 4]-code or 32-cap in PG(5,2)), using
- construction X applied to C([0,18]) ⊂ C([0,16]) [i] based on
- discarding factors / shortening the dual code based on linear OA(2241, 8225, F2, 37) (dual of [8225, 7984, 38]-code), using
Mode: 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(2242, 2056, F2, 6, 37) (dual of [(2056, 6), 12094, 38]-NRT-code) | [i] | OOA Duplication | |
| 2 | Linear OOA(2243, 2056, F2, 6, 37) (dual of [(2056, 6), 12093, 38]-NRT-code) | [i] | ||
| 3 | Linear OOA(2241, 685, F2, 42, 37) (dual of [(685, 42), 28529, 38]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |