Information on Result #548563
There is no linear OA(2196, 209, F2, 98) (dual of [209, 13, 99]-code), because construction Y1 would yield
- linear OA(2195, 205, F2, 98) (dual of [205, 10, 99]-code), but
- residual code [i] would yield linear OA(297, 106, F2, 49) (dual of [106, 9, 50]-code), but
- 1 times truncation [i] would yield linear OA(296, 105, F2, 48) (dual of [105, 9, 49]-code), but
- residual code [i] would yield linear OA(248, 56, F2, 24) (dual of [56, 8, 25]-code), but
- adding a parity check bit [i] would yield linear OA(249, 57, F2, 25) (dual of [57, 8, 26]-code), but
- “BJV†bound on codes from Brouwer’s database [i]
- adding a parity check bit [i] would yield linear OA(249, 57, F2, 25) (dual of [57, 8, 26]-code), but
- residual code [i] would yield linear OA(248, 56, F2, 24) (dual of [56, 8, 25]-code), but
- 1 times truncation [i] would yield linear OA(296, 105, F2, 48) (dual of [105, 9, 49]-code), but
- residual code [i] would yield linear OA(297, 106, F2, 49) (dual of [106, 9, 50]-code), but
- OA(213, 209, 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.
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(2197, 210, F2, 99) (dual of [210, 13, 100]-code) | [i] | Truncation | |
| 2 | No linear OOA(2197, 209, F2, 2, 99) (dual of [(209, 2), 221, 100]-NRT-code) | [i] | m-Reduction for OOAs | |
| 3 | No linear OOA(2196, 209, F2, 2, 98) (dual of [(209, 2), 222, 99]-NRT-code) | [i] | Depth Reduction | |
| 4 | No linear OOA(2196, 209, F2, 3, 98) (dual of [(209, 3), 431, 99]-NRT-code) | [i] | ||
| 5 | No linear OOA(2196, 209, F2, 4, 98) (dual of [(209, 4), 640, 99]-NRT-code) | [i] | ||
| 6 | No linear OOA(2196, 209, F2, 5, 98) (dual of [(209, 5), 849, 99]-NRT-code) | [i] | ||
| 7 | No linear OOA(2196, 209, F2, 6, 98) (dual of [(209, 6), 1058, 99]-NRT-code) | [i] | ||
| 8 | No linear OOA(2196, 209, F2, 7, 98) (dual of [(209, 7), 1267, 99]-NRT-code) | [i] | ||
| 9 | No linear OOA(2196, 209, F2, 8, 98) (dual of [(209, 8), 1476, 99]-NRT-code) | [i] | ||
| 10 | No digital (98, 196, 209)-net over F2 | [i] | Extracting Embedded Orthogonal Array | |