Information on Result #548539
There is no linear OA(2129, 141, F2, 64) (dual of [141, 12, 65]-code), because construction Y1 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
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(2130, 142, F2, 65) (dual of [142, 12, 66]-code) | [i] | Truncation | |
| 2 | No linear OOA(2130, 141, F2, 2, 65) (dual of [(141, 2), 152, 66]-NRT-code) | [i] | m-Reduction for OOAs | |
| 3 | No linear OOA(2129, 141, F2, 2, 64) (dual of [(141, 2), 153, 65]-NRT-code) | [i] | Depth Reduction | |
| 4 | No linear OOA(2129, 141, F2, 3, 64) (dual of [(141, 3), 294, 65]-NRT-code) | [i] | ||
| 5 | No linear OOA(2129, 141, F2, 4, 64) (dual of [(141, 4), 435, 65]-NRT-code) | [i] | ||
| 6 | No linear OOA(2129, 141, F2, 5, 64) (dual of [(141, 5), 576, 65]-NRT-code) | [i] | ||
| 7 | No linear OOA(2129, 141, F2, 6, 64) (dual of [(141, 6), 717, 65]-NRT-code) | [i] | ||
| 8 | No linear OOA(2129, 141, F2, 7, 64) (dual of [(141, 7), 858, 65]-NRT-code) | [i] | ||
| 9 | No linear OOA(2129, 141, F2, 8, 64) (dual of [(141, 8), 999, 65]-NRT-code) | [i] | ||
| 10 | No digital (65, 129, 141)-net over F2 | [i] | Extracting Embedded Orthogonal Array | |