Information on Result #548571
There is no linear OA(2260, 273, F2, 130) (dual of [273, 13, 131]-code), because construction Y1 would yield
- linear OA(2259, 269, F2, 130) (dual of [269, 10, 131]-code), but
- residual code [i] would yield linear OA(2129, 138, F2, 65) (dual of [138, 9, 66]-code), but
- 1 times truncation [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
- 1 times truncation [i] would yield linear OA(2128, 137, F2, 64) (dual of [137, 9, 65]-code), but
- residual code [i] would yield linear OA(2129, 138, F2, 65) (dual of [138, 9, 66]-code), but
- OA(213, 273, 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 OOA(2260, 273, F2, 2, 130) (dual of [(273, 2), 286, 131]-NRT-code) | [i] | Depth Reduction | |
| 2 | No linear OOA(2260, 273, F2, 3, 130) (dual of [(273, 3), 559, 131]-NRT-code) | [i] | ||
| 3 | No linear OOA(2260, 273, F2, 4, 130) (dual of [(273, 4), 832, 131]-NRT-code) | [i] | ||
| 4 | No linear OOA(2260, 273, F2, 5, 130) (dual of [(273, 5), 1105, 131]-NRT-code) | [i] | ||
| 5 | No linear OOA(2260, 273, F2, 6, 130) (dual of [(273, 6), 1378, 131]-NRT-code) | [i] | ||
| 6 | No linear OOA(2260, 273, F2, 7, 130) (dual of [(273, 7), 1651, 131]-NRT-code) | [i] | ||
| 7 | No linear OOA(2260, 273, F2, 8, 130) (dual of [(273, 8), 1924, 131]-NRT-code) | [i] | ||
| 8 | No digital (130, 260, 273)-net over F2 | [i] | Extracting Embedded Orthogonal Array | |