Information on Result #551306
There is no linear OOA(2103, 102, F2, 2, 57) (dual of [(102, 2), 101, 58]-NRT-code), because 9 step m-reduction would yield linear OA(294, 102, F2, 48) (dual of [102, 8, 49]-code), but
- residual code [i] would yield linear OA(246, 53, F2, 24) (dual of [53, 7, 25]-code), but
- 1 times code embedding in larger space [i] would yield linear OA(247, 54, F2, 24) (dual of [54, 7, 25]-code), but
- adding a parity check bit [i] would yield linear OA(248, 55, F2, 25) (dual of [55, 7, 26]-code), but
- “vT4†bound on codes from Brouwer’s database [i]
- adding a parity check bit [i] would yield linear OA(248, 55, F2, 25) (dual of [55, 7, 26]-code), but
- 1 times code embedding in larger space [i] would yield linear OA(247, 54, F2, 24) (dual of [54, 7, 25]-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 OOA(2103, 102, F2, 3, 57) (dual of [(102, 3), 203, 58]-NRT-code) | [i] | Depth Reduction | |
| 2 | No linear OOA(2103, 102, F2, 4, 57) (dual of [(102, 4), 305, 58]-NRT-code) | [i] | ||
| 3 | No linear OOA(2103, 102, F2, 5, 57) (dual of [(102, 5), 407, 58]-NRT-code) | [i] | ||
| 4 | No linear OOA(2103, 102, F2, 6, 57) (dual of [(102, 6), 509, 58]-NRT-code) | [i] | ||
| 5 | No linear OOA(2103, 102, F2, 7, 57) (dual of [(102, 7), 611, 58]-NRT-code) | [i] | ||
| 6 | No linear OOA(2103, 102, F2, 8, 57) (dual of [(102, 8), 713, 58]-NRT-code) | [i] | ||