Information on Result #548295
There is no linear OA(270, 77, F2, 36) (dual of [77, 7, 37]-code), because residual code would yield linear OA(234, 40, F2, 18) (dual of [40, 6, 19]-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(271, 78, F2, 37) (dual of [78, 7, 38]-code) | [i] | Truncation | |
| 2 | No linear OOA(271, 77, F2, 2, 37) (dual of [(77, 2), 83, 38]-NRT-code) | [i] | m-Reduction for OOAs | |
| 3 | No linear OOA(272, 77, F2, 2, 38) (dual of [(77, 2), 82, 39]-NRT-code) | [i] | ||
| 4 | No linear OOA(273, 77, F2, 2, 39) (dual of [(77, 2), 81, 40]-NRT-code) | [i] | ||
| 5 | No linear OOA(274, 77, F2, 2, 40) (dual of [(77, 2), 80, 41]-NRT-code) | [i] | ||
| 6 | No linear OOA(275, 77, F2, 2, 41) (dual of [(77, 2), 79, 42]-NRT-code) | [i] | ||
| 7 | No linear OOA(276, 77, F2, 2, 42) (dual of [(77, 2), 78, 43]-NRT-code) | [i] | ||
| 8 | No linear OOA(277, 77, F2, 2, 43) (dual of [(77, 2), 77, 44]-NRT-code) | [i] | ||
| 9 | No linear OOA(278, 77, F2, 2, 44) (dual of [(77, 2), 76, 45]-NRT-code) | [i] | ||
| 10 | No linear OOA(279, 77, F2, 2, 45) (dual of [(77, 2), 75, 46]-NRT-code) | [i] | ||
| 11 | No linear OOA(280, 77, F2, 2, 46) (dual of [(77, 2), 74, 47]-NRT-code) | [i] | ||
| 12 | No linear OOA(281, 77, F2, 2, 47) (dual of [(77, 2), 73, 48]-NRT-code) | [i] | ||
| 13 | No linear OOA(282, 77, F2, 2, 48) (dual of [(77, 2), 72, 49]-NRT-code) | [i] | ||
| 14 | No linear OOA(283, 77, F2, 2, 49) (dual of [(77, 2), 71, 50]-NRT-code) | [i] | ||
| 15 | No linear OOA(284, 77, F2, 2, 50) (dual of [(77, 2), 70, 51]-NRT-code) | [i] | ||
| 16 | No linear OOA(285, 77, F2, 2, 51) (dual of [(77, 2), 69, 52]-NRT-code) | [i] | ||
| 17 | No linear OOA(286, 77, F2, 2, 52) (dual of [(77, 2), 68, 53]-NRT-code) | [i] | ||
| 18 | No linear OOA(287, 77, F2, 2, 53) (dual of [(77, 2), 67, 54]-NRT-code) | [i] | ||
| 19 | No linear OOA(288, 77, F2, 2, 54) (dual of [(77, 2), 66, 55]-NRT-code) | [i] | ||
| 20 | No linear OOA(289, 77, F2, 2, 55) (dual of [(77, 2), 65, 56]-NRT-code) | [i] | ||
| 21 | No linear OOA(290, 77, F2, 2, 56) (dual of [(77, 2), 64, 57]-NRT-code) | [i] | ||
| 22 | No linear OOA(291, 77, F2, 2, 57) (dual of [(77, 2), 63, 58]-NRT-code) | [i] | ||
| 23 | No linear OOA(292, 77, F2, 2, 58) (dual of [(77, 2), 62, 59]-NRT-code) | [i] | ||
| 24 | No linear OOA(293, 77, F2, 2, 59) (dual of [(77, 2), 61, 60]-NRT-code) | [i] | ||
| 25 | No linear OOA(294, 77, F2, 2, 60) (dual of [(77, 2), 60, 61]-NRT-code) | [i] | ||
| 26 | No linear OOA(295, 77, F2, 2, 61) (dual of [(77, 2), 59, 62]-NRT-code) | [i] | ||
| 27 | No linear OOA(296, 77, F2, 2, 62) (dual of [(77, 2), 58, 63]-NRT-code) | [i] | ||
| 28 | No linear OOA(297, 77, F2, 2, 63) (dual of [(77, 2), 57, 64]-NRT-code) | [i] | ||
| 29 | No linear OOA(298, 77, F2, 2, 64) (dual of [(77, 2), 56, 65]-NRT-code) | [i] | ||
| 30 | No linear OOA(299, 77, F2, 2, 65) (dual of [(77, 2), 55, 66]-NRT-code) | [i] | ||
| 31 | No linear OOA(2100, 77, F2, 2, 66) (dual of [(77, 2), 54, 67]-NRT-code) | [i] | ||
| 32 | No linear OOA(2101, 77, F2, 2, 67) (dual of [(77, 2), 53, 68]-NRT-code) | [i] | ||
| 33 | No linear OOA(270, 77, F2, 2, 36) (dual of [(77, 2), 84, 37]-NRT-code) | [i] | Depth Reduction | |
| 34 | No linear OOA(270, 77, F2, 3, 36) (dual of [(77, 3), 161, 37]-NRT-code) | [i] | ||
| 35 | No linear OOA(270, 77, F2, 4, 36) (dual of [(77, 4), 238, 37]-NRT-code) | [i] | ||
| 36 | No linear OOA(270, 77, F2, 5, 36) (dual of [(77, 5), 315, 37]-NRT-code) | [i] | ||
| 37 | No linear OOA(270, 77, F2, 6, 36) (dual of [(77, 6), 392, 37]-NRT-code) | [i] | ||
| 38 | No linear OOA(270, 77, F2, 7, 36) (dual of [(77, 7), 469, 37]-NRT-code) | [i] | ||
| 39 | No linear OOA(270, 77, F2, 8, 36) (dual of [(77, 8), 546, 37]-NRT-code) | [i] | ||
| 40 | No digital (34, 70, 77)-net over F2 | [i] | Extracting Embedded Orthogonal Array | |
| 41 | No linear OA(2142, 150, F2, 72) (dual of [150, 8, 73]-code) | [i] | Residual Code | |