Information on Result #547717
There is no linear OA(2239, 397, F2, 106) (dual of [397, 158, 107]-code), because construction Y1 would yield
- linear OA(2238, 335, F2, 106) (dual of [335, 97, 107]-code), but
- construction Y1 [i] would yield
- OA(2237, 299, S2, 106), but
- the linear programming bound shows that M ≥ 2 372623 864838 720824 144751 616230 912568 605364 469958 081012 522169 374458 839809 772727 298051 538944 / 10 001354 293176 388857 > 2237 [i]
- OA(297, 335, S2, 36), but
- discarding factors would yield OA(297, 324, S2, 36), but
- the Rao or (dual) Hamming bound shows that M ≥ 158757 007614 184387 760434 595956 > 297 [i]
- discarding factors would yield OA(297, 324, S2, 36), but
- OA(2237, 299, S2, 106), but
- construction Y1 [i] would yield
- linear OA(2158, 397, F2, 62) (dual of [397, 239, 63]-code), but
- discarding factors / shortening the dual code would yield linear OA(2158, 391, F2, 62) (dual of [391, 233, 63]-code), but
- the improved Johnson bound shows that N ≤ 304962 143307 678590 870469 104804 226188 668017 913014 467599 614627 498245 146831 < 2233 [i]
- discarding factors / shortening the dual code would yield linear OA(2158, 391, F2, 62) (dual of [391, 233, 63]-code), but
Mode: Bound (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 | No linear OA(2240, 398, F2, 107) (dual of [398, 158, 108]-code) | [i] | Truncation | |
| 2 | No linear OOA(2240, 397, F2, 2, 107) (dual of [(397, 2), 554, 108]-NRT-code) | [i] | m-Reduction for OOAs | |
| 3 | No linear OOA(2239, 397, F2, 2, 106) (dual of [(397, 2), 555, 107]-NRT-code) | [i] | Depth Reduction | |
| 4 | No linear OOA(2239, 397, F2, 3, 106) (dual of [(397, 3), 952, 107]-NRT-code) | [i] | ||