Information on Result #548535
There is no linear OA(249, 60, F2, 24) (dual of [60, 11, 25]-code), because construction Y1 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
- linear OA(211, 60, F2, 4) (dual of [60, 49, 5]-code), but
- discarding factors / shortening the dual code would yield linear OA(211, 58, F2, 4) (dual of [58, 47, 5]-code), but
- construction Y1 [i] would yield
- linear OA(210, 34, F2, 4) (dual of [34, 24, 5]-code), but
- “BoV†bound on codes from Brouwer’s database [i]
- linear OA(247, 58, F2, 24) (dual of [58, 11, 25]-code), but
- discarding factors / shortening the dual code 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
- discarding factors / shortening the dual code would yield linear OA(247, 54, F2, 24) (dual of [54, 7, 25]-code), but
- linear OA(210, 34, F2, 4) (dual of [34, 24, 5]-code), but
- construction Y1 [i] would yield
- discarding factors / shortening the dual code would yield linear OA(211, 58, F2, 4) (dual of [58, 47, 5]-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.
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(250, 61, F2, 25) (dual of [61, 11, 26]-code) | [i] | Truncation | |
| 2 | No linear OOA(250, 60, F2, 2, 25) (dual of [(60, 2), 70, 26]-NRT-code) | [i] | m-Reduction for OOAs | |
| 3 | No linear OOA(249, 60, F2, 2, 24) (dual of [(60, 2), 71, 25]-NRT-code) | [i] | Depth Reduction | |
| 4 | No linear OOA(249, 60, F2, 3, 24) (dual of [(60, 3), 131, 25]-NRT-code) | [i] | ||
| 5 | No linear OOA(249, 60, F2, 4, 24) (dual of [(60, 4), 191, 25]-NRT-code) | [i] | ||
| 6 | No linear OOA(249, 60, F2, 5, 24) (dual of [(60, 5), 251, 25]-NRT-code) | [i] | ||
| 7 | No linear OOA(249, 60, F2, 6, 24) (dual of [(60, 6), 311, 25]-NRT-code) | [i] | ||
| 8 | No linear OOA(249, 60, F2, 7, 24) (dual of [(60, 7), 371, 25]-NRT-code) | [i] | ||
| 9 | No linear OOA(249, 60, F2, 8, 24) (dual of [(60, 8), 431, 25]-NRT-code) | [i] | ||
| 10 | No digital (25, 49, 60)-net over F2 | [i] | Extracting Embedded Orthogonal Array | |