Information on Result #551380
There is no linear OOA(2108, 112, F2, 2, 57) (dual of [(112, 2), 116, 58]-NRT-code), because 5 step m-reduction would yield linear OA(2103, 112, F2, 52) (dual of [112, 9, 53]-code), but
- residual code [i] would yield linear OA(251, 59, F2, 26) (dual of [59, 8, 27]-code), but
- adding a parity check bit [i] would yield linear OA(252, 60, F2, 27) (dual of [60, 8, 28]-code), but
- “BJV†bound on codes from Brouwer’s database [i]
- adding a parity check bit [i] would yield linear OA(252, 60, F2, 27) (dual of [60, 8, 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(2108, 112, F2, 3, 57) (dual of [(112, 3), 228, 58]-NRT-code) | [i] | Depth Reduction | |
| 2 | No linear OOA(2108, 112, F2, 4, 57) (dual of [(112, 4), 340, 58]-NRT-code) | [i] | ||
| 3 | No linear OOA(2108, 112, F2, 5, 57) (dual of [(112, 5), 452, 58]-NRT-code) | [i] | ||
| 4 | No linear OOA(2108, 112, F2, 6, 57) (dual of [(112, 6), 564, 58]-NRT-code) | [i] | ||
| 5 | No linear OOA(2108, 112, F2, 7, 57) (dual of [(112, 7), 676, 58]-NRT-code) | [i] | ||
| 6 | No linear OOA(2108, 112, F2, 8, 57) (dual of [(112, 8), 788, 58]-NRT-code) | [i] | ||