Information on Result #548045
There is no linear OA(16104, 162, F16, 97) (dual of [162, 58, 98]-code), because construction Y1 would yield
- linear OA(16103, 108, F16, 97) (dual of [108, 5, 98]-code), but
- 1 times truncation [i] would yield linear OA(16102, 107, F16, 96) (dual of [107, 5, 97]-code), but
- construction Y1 [i] would yield
- OA(16101, 103, S16, 96), but
- the (dual) Plotkin bound shows that M ≥ 4627 391781 531740 192663 407156 229397 278798 832780 749968 534992 541566 920840 538654 179420 776324 473078 006993 933138 484175 163508 129792 / 97 > 16101 [i]
- OA(165, 107, S16, 4), but
- discarding factors would yield OA(165, 97, S16, 4), but
- the Rao or (dual) Hamming bound shows that M ≥ 1 049056 > 165 [i]
- discarding factors would yield OA(165, 97, S16, 4), but
- OA(16101, 103, S16, 96), but
- construction Y1 [i] would yield
- 1 times truncation [i] would yield linear OA(16102, 107, F16, 96) (dual of [107, 5, 97]-code), but
- OA(1658, 162, S16, 54), but
- the linear programming bound shows that M ≥ 2392 777823 419786 866364 559380 339374 056579 306009 003848 144643 063934 367870 574320 891182 422286 906379 206656 / 330470 333340 946429 385565 160481 > 1658 [i]
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(16104, 162, F16, 2, 97) (dual of [(162, 2), 220, 98]-NRT-code) | [i] | Depth Reduction | |