Information on Result #554242
There is no linear OOA(2224, 215, F2, 2, 122) (dual of [(215, 2), 206, 123]-NRT-code), because 18 step m-reduction would yield linear OA(2206, 215, F2, 104) (dual of [215, 9, 105]-code), but
- residual code [i] 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
- residual code [i] would yield linear OA(250, 57, F2, 26) (dual of [57, 7, 27]-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(2224, 215, F2, 3, 122) (dual of [(215, 3), 421, 123]-NRT-code) | [i] | Depth Reduction | |
| 2 | No linear OOA(2224, 215, F2, 4, 122) (dual of [(215, 4), 636, 123]-NRT-code) | [i] | ||
| 3 | No linear OOA(2224, 215, F2, 5, 122) (dual of [(215, 5), 851, 123]-NRT-code) | [i] | ||
| 4 | No linear OOA(2224, 215, F2, 6, 122) (dual of [(215, 6), 1066, 123]-NRT-code) | [i] | ||
| 5 | No linear OOA(2224, 215, F2, 7, 122) (dual of [(215, 7), 1281, 123]-NRT-code) | [i] | ||
| 6 | No linear OOA(2224, 215, F2, 8, 122) (dual of [(215, 8), 1496, 123]-NRT-code) | [i] | ||