Information on Result #547715
There is no linear OA(2235, 396, F2, 104) (dual of [396, 161, 105]-code), because construction Y1 would yield
- linear OA(2234, 332, F2, 104) (dual of [332, 98, 105]-code), but
- construction Y1 [i] would yield
- OA(2233, 296, S2, 104), but
- the linear programming bound shows that M ≥ 40 441027 764911 159411 999678 250893 328460 000589 698723 782371 054222 923004 931887 671319 124733 067264 / 2499 525994 551277 812375 > 2233 [i]
- linear OA(298, 332, F2, 36) (dual of [332, 234, 37]-code), but
- discarding factors / shortening the dual code would yield linear OA(298, 328, F2, 36) (dual of [328, 230, 37]-code), but
- the Johnson bound shows that N ≤ 1638 846907 564815 429866 669910 715625 391366 929534 207151 722672 384476 916602 < 2230 [i]
- discarding factors / shortening the dual code would yield linear OA(298, 328, F2, 36) (dual of [328, 230, 37]-code), but
- OA(2233, 296, S2, 104), but
- construction Y1 [i] would yield
- linear OA(2161, 396, F2, 64) (dual of [396, 235, 65]-code), but
- discarding factors / shortening the dual code would yield linear OA(2161, 386, F2, 64) (dual of [386, 225, 65]-code), but
- the improved Johnson bound shows that N ≤ 1273 433173 266206 536946 189159 627310 843674 819540 383544 656821 436068 911665 < 2225 [i]
- discarding factors / shortening the dual code would yield linear OA(2161, 386, F2, 64) (dual of [386, 225, 65]-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(2236, 397, F2, 105) (dual of [397, 161, 106]-code) | [i] | Truncation | |
| 2 | No linear OOA(2236, 396, F2, 2, 105) (dual of [(396, 2), 556, 106]-NRT-code) | [i] | m-Reduction for OOAs | |
| 3 | No linear OOA(2235, 396, F2, 2, 104) (dual of [(396, 2), 557, 105]-NRT-code) | [i] | Depth Reduction | |