Information on Result #2156221
There is no linear OA(251, 59, F2, 26) (dual of [59, 8, 27]-code), because adding a parity check bit would yield linear OA(252, 60, F2, 27) (dual of [60, 8, 28]-code), but
- “BJV†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 OOA(252, 59, F2, 2, 27) (dual of [(59, 2), 66, 28]-NRT-code) | [i] | m-Reduction for OOAs | |
| 2 | No linear OOA(253, 59, F2, 2, 28) (dual of [(59, 2), 65, 29]-NRT-code) | [i] | ||
| 3 | No linear OOA(254, 59, F2, 2, 29) (dual of [(59, 2), 64, 30]-NRT-code) | [i] | ||
| 4 | No linear OOA(255, 59, F2, 2, 30) (dual of [(59, 2), 63, 31]-NRT-code) | [i] | ||
| 5 | No linear OOA(256, 59, F2, 2, 31) (dual of [(59, 2), 62, 32]-NRT-code) | [i] | ||
| 6 | No linear OOA(257, 59, F2, 2, 32) (dual of [(59, 2), 61, 33]-NRT-code) | [i] | ||
| 7 | No linear OOA(258, 59, F2, 2, 33) (dual of [(59, 2), 60, 34]-NRT-code) | [i] | ||
| 8 | No linear OOA(259, 59, F2, 2, 34) (dual of [(59, 2), 59, 35]-NRT-code) | [i] | ||
| 9 | No linear OOA(260, 59, F2, 2, 35) (dual of [(59, 2), 58, 36]-NRT-code) | [i] | ||
| 10 | No linear OOA(261, 59, F2, 2, 36) (dual of [(59, 2), 57, 37]-NRT-code) | [i] | ||
| 11 | No linear OOA(262, 59, F2, 2, 37) (dual of [(59, 2), 56, 38]-NRT-code) | [i] | ||
| 12 | No linear OOA(263, 59, F2, 2, 38) (dual of [(59, 2), 55, 39]-NRT-code) | [i] | ||
| 13 | No linear OOA(264, 59, F2, 2, 39) (dual of [(59, 2), 54, 40]-NRT-code) | [i] | ||
| 14 | No linear OOA(265, 59, F2, 2, 40) (dual of [(59, 2), 53, 41]-NRT-code) | [i] | ||
| 15 | No linear OOA(266, 59, F2, 2, 41) (dual of [(59, 2), 52, 42]-NRT-code) | [i] | ||
| 16 | No linear OOA(267, 59, F2, 2, 42) (dual of [(59, 2), 51, 43]-NRT-code) | [i] | ||
| 17 | No linear OOA(268, 59, F2, 2, 43) (dual of [(59, 2), 50, 44]-NRT-code) | [i] | ||
| 18 | No linear OOA(269, 59, F2, 2, 44) (dual of [(59, 2), 49, 45]-NRT-code) | [i] | ||
| 19 | No linear OOA(270, 59, F2, 2, 45) (dual of [(59, 2), 48, 46]-NRT-code) | [i] | ||
| 20 | No linear OOA(271, 59, F2, 2, 46) (dual of [(59, 2), 47, 47]-NRT-code) | [i] | ||
| 21 | No linear OOA(272, 59, F2, 2, 47) (dual of [(59, 2), 46, 48]-NRT-code) | [i] | ||
| 22 | No linear OOA(273, 59, F2, 2, 48) (dual of [(59, 2), 45, 49]-NRT-code) | [i] | ||
| 23 | No linear OOA(274, 59, F2, 2, 49) (dual of [(59, 2), 44, 50]-NRT-code) | [i] | ||
| 24 | No linear OOA(275, 59, F2, 2, 50) (dual of [(59, 2), 43, 51]-NRT-code) | [i] | ||
| 25 | No linear OOA(276, 59, F2, 2, 51) (dual of [(59, 2), 42, 52]-NRT-code) | [i] | ||
| 26 | No linear OOA(251, 59, F2, 2, 26) (dual of [(59, 2), 67, 27]-NRT-code) | [i] | Depth Reduction | |
| 27 | No linear OOA(251, 59, F2, 3, 26) (dual of [(59, 3), 126, 27]-NRT-code) | [i] | ||
| 28 | No linear OOA(251, 59, F2, 4, 26) (dual of [(59, 4), 185, 27]-NRT-code) | [i] | ||
| 29 | No linear OOA(251, 59, F2, 5, 26) (dual of [(59, 5), 244, 27]-NRT-code) | [i] | ||
| 30 | No linear OOA(251, 59, F2, 6, 26) (dual of [(59, 6), 303, 27]-NRT-code) | [i] | ||
| 31 | No linear OOA(251, 59, F2, 7, 26) (dual of [(59, 7), 362, 27]-NRT-code) | [i] | ||
| 32 | No linear OOA(251, 59, F2, 8, 26) (dual of [(59, 8), 421, 27]-NRT-code) | [i] | ||
| 33 | No digital (25, 51, 59)-net over F2 | [i] | Extracting Embedded Orthogonal Array | |
| 34 | No linear OA(2103, 112, F2, 52) (dual of [112, 9, 53]-code) | [i] | Residual Code | |