Information on Result #2156737
There is no linear OA(2130, 142, F2, 65) (dual of [142, 12, 66]-code), because 1 times truncation would yield linear OA(2129, 141, F2, 64) (dual of [141, 12, 65]-code), but
- construction Y1 [i] would yield
- linear OA(2128, 137, F2, 64) (dual of [137, 9, 65]-code), but
- residual code [i] would yield linear OA(264, 72, F2, 32) (dual of [72, 8, 33]-code), but
- adding a parity check bit [i] would yield linear OA(265, 73, F2, 33) (dual of [73, 8, 34]-code), but
- “BJV†bound on codes from Brouwer’s database [i]
- adding a parity check bit [i] would yield linear OA(265, 73, F2, 33) (dual of [73, 8, 34]-code), but
- residual code [i] would yield linear OA(264, 72, F2, 32) (dual of [72, 8, 33]-code), but
- OA(212, 141, S2, 4), but
- discarding factors would yield OA(212, 91, S2, 4), but
- the Rao or (dual) Hamming bound shows that M ≥ 4187 > 212 [i]
- discarding factors would yield OA(212, 91, S2, 4), but
- linear OA(2128, 137, F2, 64) (dual of [137, 9, 65]-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.
Compare with Markus Grassl’s online database of code parameters.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | No linear OA(2260, 275, F2, 130) (dual of [275, 15, 131]-code) | [i] | Residual Code | |