Information on Result #553512
There is no linear OOA(2198, 205, F2, 2, 101) (dual of [(205, 2), 212, 102]-NRT-code), because 3 step m-reduction would yield linear OA(2195, 205, F2, 98) (dual of [205, 10, 99]-code), but
- residual code [i] would yield linear OA(297, 106, F2, 49) (dual of [106, 9, 50]-code), but
- 1 times truncation [i] would yield linear OA(296, 105, F2, 48) (dual of [105, 9, 49]-code), but
- residual code [i] would yield linear OA(248, 56, F2, 24) (dual of [56, 8, 25]-code), but
- adding a parity check bit [i] would yield linear OA(249, 57, F2, 25) (dual of [57, 8, 26]-code), but
- “BJV†bound on codes from Brouwer’s database [i]
- adding a parity check bit [i] would yield linear OA(249, 57, F2, 25) (dual of [57, 8, 26]-code), but
- residual code [i] would yield linear OA(248, 56, F2, 24) (dual of [56, 8, 25]-code), but
- 1 times truncation [i] would yield linear OA(296, 105, F2, 48) (dual of [105, 9, 49]-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(2198, 205, F2, 3, 101) (dual of [(205, 3), 417, 102]-NRT-code) | [i] | Depth Reduction | |
| 2 | No linear OOA(2198, 205, F2, 4, 101) (dual of [(205, 4), 622, 102]-NRT-code) | [i] | ||
| 3 | No linear OOA(2198, 205, F2, 5, 101) (dual of [(205, 5), 827, 102]-NRT-code) | [i] | ||
| 4 | No linear OOA(2198, 205, F2, 6, 101) (dual of [(205, 6), 1032, 102]-NRT-code) | [i] | ||
| 5 | No linear OOA(2198, 205, F2, 7, 101) (dual of [(205, 7), 1237, 102]-NRT-code) | [i] | ||
| 6 | No linear OOA(2198, 205, F2, 8, 101) (dual of [(205, 8), 1442, 102]-NRT-code) | [i] | ||