Information on Result #548556
There is no linear OA(2175, 260, F2, 82) (dual of [260, 85, 83]-code), because construction Y1 would yield
- linear OA(2174, 228, F2, 82) (dual of [228, 54, 83]-code), but
- construction Y1 [i] would yield
- linear OA(2173, 208, F2, 82) (dual of [208, 35, 83]-code), but
- construction Y1 [i] would yield
- linear OA(2172, 196, F2, 82) (dual of [196, 24, 83]-code), but
- adding a parity check bit [i] would yield linear OA(2173, 197, F2, 83) (dual of [197, 24, 84]-code), but
- OA(235, 208, S2, 12), but
- discarding factors would yield OA(235, 173, S2, 12), but
- the Rao or (dual) Hamming bound shows that M ≥ 35365 229344 > 235 [i]
- discarding factors would yield OA(235, 173, S2, 12), but
- linear OA(2172, 196, F2, 82) (dual of [196, 24, 83]-code), but
- construction Y1 [i] would yield
- OA(254, 228, S2, 20), but
- discarding factors would yield OA(254, 195, S2, 20), but
- the Rao or (dual) Hamming bound shows that M ≥ 18304 094847 646336 > 254 [i]
- discarding factors would yield OA(254, 195, S2, 20), but
- linear OA(2173, 208, F2, 82) (dual of [208, 35, 83]-code), but
- construction Y1 [i] would yield
- linear OA(285, 260, F2, 32) (dual of [260, 175, 33]-code), but
- discarding factors / shortening the dual code would yield linear OA(285, 258, F2, 32) (dual of [258, 173, 33]-code), but
- the improved Johnson bound shows that N ≤ 22615 861090 934062 894456 565101 208250 515374 333379 910527 < 2173 [i]
- discarding factors / shortening the dual code would yield linear OA(285, 258, F2, 32) (dual of [258, 173, 33]-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(2176, 261, F2, 83) (dual of [261, 85, 84]-code) | [i] | Truncation | |
| 2 | No linear OOA(2176, 260, F2, 2, 83) (dual of [(260, 2), 344, 84]-NRT-code) | [i] | m-Reduction for OOAs | |
| 3 | No linear OOA(2175, 260, F2, 2, 82) (dual of [(260, 2), 345, 83]-NRT-code) | [i] | Depth Reduction | |