Information on Result #548568
There is no linear OA(2257, 270, F2, 128) (dual of [270, 13, 129]-code), because construction Y1 would yield
- linear OA(2256, 266, F2, 128) (dual of [266, 10, 129]-code), but
- residual code [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
- residual code [i] would yield linear OA(2128, 137, F2, 64) (dual of [137, 9, 65]-code), but
- OA(213, 270, S2, 4), but
- discarding factors would yield OA(213, 128, S2, 4), but
- the Rao or (dual) Hamming bound shows that M ≥ 8257 > 213 [i]
- discarding factors would yield OA(213, 128, 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.
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, 271, F2, 129) (dual of [271, 13, 130]-code) | [i] | Truncation | |
| 2 | No linear OOA(2258, 270, F2, 2, 129) (dual of [(270, 2), 282, 130]-NRT-code) | [i] | m-Reduction for OOAs | |
| 3 | No linear OOA(2257, 270, F2, 2, 128) (dual of [(270, 2), 283, 129]-NRT-code) | [i] | Depth Reduction | |
| 4 | No linear OOA(2257, 270, F2, 3, 128) (dual of [(270, 3), 553, 129]-NRT-code) | [i] | ||
| 5 | No linear OOA(2257, 270, F2, 4, 128) (dual of [(270, 4), 823, 129]-NRT-code) | [i] | ||
| 6 | No linear OOA(2257, 270, F2, 5, 128) (dual of [(270, 5), 1093, 129]-NRT-code) | [i] | ||
| 7 | No linear OOA(2257, 270, F2, 6, 128) (dual of [(270, 6), 1363, 129]-NRT-code) | [i] | ||
| 8 | No linear OOA(2257, 270, F2, 7, 128) (dual of [(270, 7), 1633, 129]-NRT-code) | [i] | ||
| 9 | No linear OOA(2257, 270, F2, 8, 128) (dual of [(270, 8), 1903, 129]-NRT-code) | [i] | ||
| 10 | No digital (129, 257, 270)-net over F2 | [i] | Extracting Embedded Orthogonal Array | |