Information on Result #548561
There is no linear OA(2193, 206, F2, 96) (dual of [206, 13, 97]-code), because construction Y1 would yield
- linear OA(2192, 202, F2, 96) (dual of [202, 10, 97]-code), but
- residual code [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
- residual code [i] would yield linear OA(296, 105, F2, 48) (dual of [105, 9, 49]-code), but
- OA(213, 206, 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(2194, 207, F2, 97) (dual of [207, 13, 98]-code) | [i] | Truncation | |
| 2 | No linear OOA(2194, 206, F2, 2, 97) (dual of [(206, 2), 218, 98]-NRT-code) | [i] | m-Reduction for OOAs | |
| 3 | No linear OOA(2193, 206, F2, 2, 96) (dual of [(206, 2), 219, 97]-NRT-code) | [i] | Depth Reduction | |
| 4 | No linear OOA(2193, 206, F2, 3, 96) (dual of [(206, 3), 425, 97]-NRT-code) | [i] | ||
| 5 | No linear OOA(2193, 206, F2, 4, 96) (dual of [(206, 4), 631, 97]-NRT-code) | [i] | ||
| 6 | No linear OOA(2193, 206, F2, 5, 96) (dual of [(206, 5), 837, 97]-NRT-code) | [i] | ||
| 7 | No linear OOA(2193, 206, F2, 6, 96) (dual of [(206, 6), 1043, 97]-NRT-code) | [i] | ||
| 8 | No linear OOA(2193, 206, F2, 7, 96) (dual of [(206, 7), 1249, 97]-NRT-code) | [i] | ||
| 9 | No linear OOA(2193, 206, F2, 8, 96) (dual of [(206, 8), 1455, 97]-NRT-code) | [i] | ||
| 10 | No digital (97, 193, 206)-net over F2 | [i] | Extracting Embedded Orthogonal Array | |