Information on Result #2156217
There is no linear OA(247, 54, F2, 24) (dual of [54, 7, 25]-code), because adding a parity check bit would yield linear OA(248, 55, F2, 25) (dual of [55, 7, 26]-code), but
- “vT4†bound on codes from Brouwer’s database [i]
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(247, 54, F2, 25) (dual of [54, 7, 26]-code) | [i] | Strength Reduction | |
| 2 | No linear OA(246, 53, F2, 24) (dual of [53, 7, 25]-code) | [i] | Code Embedding in Larger Space | |
| 3 | No linear OA(249, 56, F2, 26) (dual of [56, 7, 27]-code) | [i] | Truncation | |
| 4 | No linear OA(250, 57, F2, 27) (dual of [57, 7, 28]-code) | [i] | ||
| 5 | No linear OOA(248, 54, F2, 2, 25) (dual of [(54, 2), 60, 26]-NRT-code) | [i] | m-Reduction for OOAs | |
| 6 | No linear OOA(249, 54, F2, 2, 26) (dual of [(54, 2), 59, 27]-NRT-code) | [i] | ||
| 7 | No linear OOA(250, 54, F2, 2, 27) (dual of [(54, 2), 58, 28]-NRT-code) | [i] | ||
| 8 | No linear OOA(251, 54, F2, 2, 28) (dual of [(54, 2), 57, 29]-NRT-code) | [i] | ||
| 9 | No linear OOA(252, 54, F2, 2, 29) (dual of [(54, 2), 56, 30]-NRT-code) | [i] | ||
| 10 | No linear OOA(253, 54, F2, 2, 30) (dual of [(54, 2), 55, 31]-NRT-code) | [i] | ||
| 11 | No linear OOA(254, 54, F2, 2, 31) (dual of [(54, 2), 54, 32]-NRT-code) | [i] | ||
| 12 | No linear OOA(255, 54, F2, 2, 32) (dual of [(54, 2), 53, 33]-NRT-code) | [i] | ||
| 13 | No linear OOA(256, 54, F2, 2, 33) (dual of [(54, 2), 52, 34]-NRT-code) | [i] | ||
| 14 | No linear OOA(257, 54, F2, 2, 34) (dual of [(54, 2), 51, 35]-NRT-code) | [i] | ||
| 15 | No linear OOA(258, 54, F2, 2, 35) (dual of [(54, 2), 50, 36]-NRT-code) | [i] | ||
| 16 | No linear OOA(259, 54, F2, 2, 36) (dual of [(54, 2), 49, 37]-NRT-code) | [i] | ||
| 17 | No linear OOA(260, 54, F2, 2, 37) (dual of [(54, 2), 48, 38]-NRT-code) | [i] | ||
| 18 | No linear OOA(261, 54, F2, 2, 38) (dual of [(54, 2), 47, 39]-NRT-code) | [i] | ||
| 19 | No linear OOA(262, 54, F2, 2, 39) (dual of [(54, 2), 46, 40]-NRT-code) | [i] | ||
| 20 | No linear OOA(263, 54, F2, 2, 40) (dual of [(54, 2), 45, 41]-NRT-code) | [i] | ||
| 21 | No linear OOA(264, 54, F2, 2, 41) (dual of [(54, 2), 44, 42]-NRT-code) | [i] | ||
| 22 | No linear OOA(265, 54, F2, 2, 42) (dual of [(54, 2), 43, 43]-NRT-code) | [i] | ||
| 23 | No linear OOA(266, 54, F2, 2, 43) (dual of [(54, 2), 42, 44]-NRT-code) | [i] | ||
| 24 | No linear OOA(267, 54, F2, 2, 44) (dual of [(54, 2), 41, 45]-NRT-code) | [i] | ||
| 25 | No linear OOA(268, 54, F2, 2, 45) (dual of [(54, 2), 40, 46]-NRT-code) | [i] | ||
| 26 | No linear OOA(269, 54, F2, 2, 46) (dual of [(54, 2), 39, 47]-NRT-code) | [i] | ||
| 27 | No linear OOA(270, 54, F2, 2, 47) (dual of [(54, 2), 38, 48]-NRT-code) | [i] | ||
| 28 | No linear OOA(271, 54, F2, 2, 48) (dual of [(54, 2), 37, 49]-NRT-code) | [i] | ||
| 29 | No linear OOA(247, 54, F2, 2, 24) (dual of [(54, 2), 61, 25]-NRT-code) | [i] | Depth Reduction | |
| 30 | No linear OOA(247, 54, F2, 3, 24) (dual of [(54, 3), 115, 25]-NRT-code) | [i] | ||
| 31 | No linear OOA(247, 54, F2, 4, 24) (dual of [(54, 4), 169, 25]-NRT-code) | [i] | ||
| 32 | No linear OOA(247, 54, F2, 5, 24) (dual of [(54, 5), 223, 25]-NRT-code) | [i] | ||
| 33 | No linear OOA(247, 54, F2, 6, 24) (dual of [(54, 6), 277, 25]-NRT-code) | [i] | ||
| 34 | No linear OOA(247, 54, F2, 7, 24) (dual of [(54, 7), 331, 25]-NRT-code) | [i] | ||
| 35 | No linear OOA(247, 54, F2, 8, 24) (dual of [(54, 8), 385, 25]-NRT-code) | [i] | ||
| 36 | No digital (23, 47, 54)-net over F2 | [i] | Extracting Embedded Orthogonal Array | |
| 37 | No linear OA(295, 103, F2, 48) (dual of [103, 8, 49]-code) | [i] | Residual Code | |
| 38 | No linear OA(211, 58, F2, 4) (dual of [58, 47, 5]-code) | [i] | Construction Y1 (Bound) | |