Information on Result #547729
There is no linear OA(2257, 294, F2, 126) (dual of [294, 37, 127]-code), because construction Y1 would yield
- linear OA(2256, 282, F2, 126) (dual of [282, 26, 127]-code), but
- construction Y1 [i] would yield
- linear OA(2255, 274, F2, 126) (dual of [274, 19, 127]-code), but
- residual code [i] would yield OA(2129, 147, S2, 63), but
- 1 times truncation [i] would yield OA(2128, 146, S2, 62), but
- the linear programming bound shows that M ≥ 10 546031 115613 724859 656905 833525 360409 444352 / 30229 > 2128 [i]
- 1 times truncation [i] would yield OA(2128, 146, S2, 62), but
- residual code [i] would yield OA(2129, 147, S2, 63), but
- OA(226, 282, S2, 8), but
- discarding factors would yield OA(226, 201, S2, 8), but
- the Rao or (dual) Hamming bound shows that M ≥ 67 351952 > 226 [i]
- discarding factors would yield OA(226, 201, S2, 8), but
- linear OA(2255, 274, F2, 126) (dual of [274, 19, 127]-code), but
- construction Y1 [i] would yield
- OA(237, 294, S2, 12), but
- discarding factors would yield OA(237, 217, S2, 12), but
- the Rao or (dual) Hamming bound shows that M ≥ 139173 045698 > 237 [i]
- discarding factors would yield OA(237, 217, S2, 12), 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 OA(2258, 312, F2, 126) (dual of [312, 54, 127]-code) | [i] | Construction Y1 (Bound) | |