Information on Result #548433
There is no linear OA(2256, 266, F2, 128) (dual of [266, 10, 129]-code), because residual code 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
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(2257, 267, F2, 129) (dual of [267, 10, 130]-code) | [i] | Truncation | |
| 2 | No linear OA(2259, 269, F2, 131) (dual of [269, 10, 132]-code) | [i] | ||
| 3 | No linear OOA(2257, 266, F2, 2, 129) (dual of [(266, 2), 275, 130]-NRT-code) | [i] | m-Reduction for OOAs | |
| 4 | No linear OOA(2258, 266, F2, 2, 130) (dual of [(266, 2), 274, 131]-NRT-code) | [i] | ||
| 5 | No linear OOA(2259, 266, F2, 2, 131) (dual of [(266, 2), 273, 132]-NRT-code) | [i] | ||
| 6 | No linear OOA(2260, 266, F2, 2, 132) (dual of [(266, 2), 272, 133]-NRT-code) | [i] | ||
| 7 | No linear OOA(2256, 266, F2, 2, 128) (dual of [(266, 2), 276, 129]-NRT-code) | [i] | Depth Reduction | |
| 8 | No linear OOA(2256, 266, F2, 3, 128) (dual of [(266, 3), 542, 129]-NRT-code) | [i] | ||
| 9 | No linear OOA(2256, 266, F2, 4, 128) (dual of [(266, 4), 808, 129]-NRT-code) | [i] | ||
| 10 | No linear OOA(2256, 266, F2, 5, 128) (dual of [(266, 5), 1074, 129]-NRT-code) | [i] | ||
| 11 | No linear OOA(2256, 266, F2, 6, 128) (dual of [(266, 6), 1340, 129]-NRT-code) | [i] | ||
| 12 | No linear OOA(2256, 266, F2, 7, 128) (dual of [(266, 7), 1606, 129]-NRT-code) | [i] | ||
| 13 | No linear OOA(2256, 266, F2, 8, 128) (dual of [(266, 8), 1872, 129]-NRT-code) | [i] | ||
| 14 | No digital (128, 256, 266)-net over F2 | [i] | Extracting Embedded Orthogonal Array | |
| 15 | No linear OA(2257, 270, F2, 128) (dual of [270, 13, 129]-code) | [i] | Construction Y1 (Bound) | |