Information on Result #551367
There is no linear OOA(2107, 110, F2, 2, 57) (dual of [(110, 2), 113, 58]-NRT-code), because 5 step m-reduction would yield linear OA(2102, 110, F2, 52) (dual of [110, 8, 53]-code), but
- residual code [i] would yield linear OA(250, 57, F2, 26) (dual of [57, 7, 27]-code), but
- adding a parity check bit [i] would yield linear OA(251, 58, F2, 27) (dual of [58, 7, 28]-code), but
- “vT3†bound on codes from Brouwer’s database [i]
- adding a parity check bit [i] would yield linear OA(251, 58, F2, 27) (dual of [58, 7, 28]-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(2107, 110, F2, 3, 57) (dual of [(110, 3), 223, 58]-NRT-code) | [i] | Depth Reduction | |
| 2 | No linear OOA(2107, 110, F2, 4, 57) (dual of [(110, 4), 333, 58]-NRT-code) | [i] | ||
| 3 | No linear OOA(2107, 110, F2, 5, 57) (dual of [(110, 5), 443, 58]-NRT-code) | [i] | ||
| 4 | No linear OOA(2107, 110, F2, 6, 57) (dual of [(110, 6), 553, 58]-NRT-code) | [i] | ||
| 5 | No linear OOA(2107, 110, F2, 7, 57) (dual of [(110, 7), 663, 58]-NRT-code) | [i] | ||
| 6 | No linear OOA(2107, 110, F2, 8, 57) (dual of [(110, 8), 773, 58]-NRT-code) | [i] | ||