Information on Result #552801
There is no linear OOA(2175, 228, F2, 2, 83) (dual of [(228, 2), 281, 84]-NRT-code), because 1 step m-reduction 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
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 OOA(2175, 228, F2, 3, 83) (dual of [(228, 3), 509, 84]-NRT-code) | [i] | Depth Reduction | |
| 2 | No linear OOA(2175, 228, F2, 4, 83) (dual of [(228, 4), 737, 84]-NRT-code) | [i] | ||
| 3 | No linear OOA(2175, 228, F2, 5, 83) (dual of [(228, 5), 965, 84]-NRT-code) | [i] | ||
| 4 | No linear OOA(2175, 228, F2, 6, 83) (dual of [(228, 6), 1193, 84]-NRT-code) | [i] | ||
| 5 | No linear OOA(2175, 228, F2, 7, 83) (dual of [(228, 7), 1421, 84]-NRT-code) | [i] | ||
| 6 | No linear OOA(2175, 228, F2, 8, 83) (dual of [(228, 8), 1649, 84]-NRT-code) | [i] | ||