Information on Result #547701
There is no linear OA(2197, 371, F2, 84) (dual of [371, 174, 85]-code), because construction Y1 would yield
- OA(2196, 299, S2, 84), but
- adding a parity check bit [i] would yield OA(2197, 300, S2, 85), but
- the linear programming bound shows that M ≥ 333445 596634 842101 957662 761369 966680 970228 955880 375209 681209 067512 159971 176505 925710 036206 046927 475988 200870 117376 / 1 055603 696799 631985 996897 950925 994087 362055 971326 408581 > 2197 [i]
- adding a parity check bit [i] would yield OA(2197, 300, S2, 85), but
- linear OA(2174, 371, F2, 72) (dual of [371, 197, 73]-code), but
- discarding factors / shortening the dual code would yield linear OA(2174, 369, F2, 72) (dual of [369, 195, 73]-code), but
- the improved Johnson bound shows that N ≤ 4 762310 927785 440214 696531 636051 250217 829991 363521 204568 820627 < 2195 [i]
- discarding factors / shortening the dual code would yield linear OA(2174, 369, F2, 72) (dual of [369, 195, 73]-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(2198, 372, F2, 85) (dual of [372, 174, 86]-code) | [i] | Truncation | |
| 2 | No linear OOA(2198, 371, F2, 2, 85) (dual of [(371, 2), 544, 86]-NRT-code) | [i] | m-Reduction for OOAs | |
| 3 | No linear OOA(2197, 371, F2, 2, 84) (dual of [(371, 2), 545, 85]-NRT-code) | [i] | Depth Reduction | |