Information on Result #551700
There is no linear OOA(2128, 127, F2, 2, 70) (dual of [(127, 2), 126, 71]-NRT-code), because 10 step m-reduction would yield linear OA(2118, 127, F2, 60) (dual of [127, 9, 61]-code), but
- residual code [i] would yield linear OA(258, 66, F2, 30) (dual of [66, 8, 31]-code), but
- adding a parity check bit [i] would yield linear OA(259, 67, F2, 31) (dual of [67, 8, 32]-code), but
- “DHM†bound on codes from Brouwer’s database [i]
- adding a parity check bit [i] would yield linear OA(259, 67, F2, 31) (dual of [67, 8, 32]-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(2128, 127, F2, 3, 70) (dual of [(127, 3), 253, 71]-NRT-code) | [i] | Depth Reduction | |
| 2 | No linear OOA(2128, 127, F2, 4, 70) (dual of [(127, 4), 380, 71]-NRT-code) | [i] | ||
| 3 | No linear OOA(2128, 127, F2, 5, 70) (dual of [(127, 5), 507, 71]-NRT-code) | [i] | ||
| 4 | No linear OOA(2128, 127, F2, 6, 70) (dual of [(127, 6), 634, 71]-NRT-code) | [i] | ||
| 5 | No linear OOA(2128, 127, F2, 7, 70) (dual of [(127, 7), 761, 71]-NRT-code) | [i] | ||
| 6 | No linear OOA(2128, 127, F2, 8, 70) (dual of [(127, 8), 888, 71]-NRT-code) | [i] | ||