Information on Result #547100
There is no linear OA(436, 40, F4, 28) (dual of [40, 4, 29]-code), because residual code would yield linear OA(48, 11, F4, 7) (dual of [11, 3, 8]-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(437, 41, F4, 29) (dual of [41, 4, 30]-code) | [i] | Truncation | |
| 2 | No linear OA(438, 42, F4, 30) (dual of [42, 4, 31]-code) | [i] | ||
| 3 | No linear OA(439, 43, F4, 31) (dual of [43, 4, 32]-code) | [i] | ||
| 4 | No linear OOA(437, 40, F4, 2, 29) (dual of [(40, 2), 43, 30]-NRT-code) | [i] | m-Reduction for OOAs | |
| 5 | No linear OOA(438, 40, F4, 2, 30) (dual of [(40, 2), 42, 31]-NRT-code) | [i] | ||
| 6 | No linear OOA(439, 40, F4, 2, 31) (dual of [(40, 2), 41, 32]-NRT-code) | [i] | ||
| 7 | No linear OOA(440, 40, F4, 2, 32) (dual of [(40, 2), 40, 33]-NRT-code) | [i] | ||
| 8 | No linear OOA(441, 40, F4, 2, 33) (dual of [(40, 2), 39, 34]-NRT-code) | [i] | ||
| 9 | No linear OOA(442, 40, F4, 2, 34) (dual of [(40, 2), 38, 35]-NRT-code) | [i] | ||
| 10 | No linear OOA(443, 40, F4, 2, 35) (dual of [(40, 2), 37, 36]-NRT-code) | [i] | ||
| 11 | No linear OOA(444, 40, F4, 2, 36) (dual of [(40, 2), 36, 37]-NRT-code) | [i] | ||
| 12 | No linear OOA(445, 40, F4, 2, 37) (dual of [(40, 2), 35, 38]-NRT-code) | [i] | ||
| 13 | No linear OOA(446, 40, F4, 2, 38) (dual of [(40, 2), 34, 39]-NRT-code) | [i] | ||
| 14 | No linear OOA(447, 40, F4, 2, 39) (dual of [(40, 2), 33, 40]-NRT-code) | [i] | ||
| 15 | No linear OOA(448, 40, F4, 2, 40) (dual of [(40, 2), 32, 41]-NRT-code) | [i] | ||
| 16 | No linear OOA(449, 40, F4, 2, 41) (dual of [(40, 2), 31, 42]-NRT-code) | [i] | ||
| 17 | No linear OOA(450, 40, F4, 2, 42) (dual of [(40, 2), 30, 43]-NRT-code) | [i] | ||
| 18 | No linear OOA(451, 40, F4, 2, 43) (dual of [(40, 2), 29, 44]-NRT-code) | [i] | ||
| 19 | No linear OOA(452, 40, F4, 2, 44) (dual of [(40, 2), 28, 45]-NRT-code) | [i] | ||
| 20 | No linear OOA(453, 40, F4, 2, 45) (dual of [(40, 2), 27, 46]-NRT-code) | [i] | ||
| 21 | No linear OOA(454, 40, F4, 2, 46) (dual of [(40, 2), 26, 47]-NRT-code) | [i] | ||
| 22 | No linear OOA(455, 40, F4, 2, 47) (dual of [(40, 2), 25, 48]-NRT-code) | [i] | ||
| 23 | No linear OOA(456, 40, F4, 2, 48) (dual of [(40, 2), 24, 49]-NRT-code) | [i] | ||
| 24 | No linear OOA(457, 40, F4, 2, 49) (dual of [(40, 2), 23, 50]-NRT-code) | [i] | ||
| 25 | No linear OOA(458, 40, F4, 2, 50) (dual of [(40, 2), 22, 51]-NRT-code) | [i] | ||
| 26 | No linear OOA(459, 40, F4, 2, 51) (dual of [(40, 2), 21, 52]-NRT-code) | [i] | ||
| 27 | No linear OOA(460, 40, F4, 2, 52) (dual of [(40, 2), 20, 53]-NRT-code) | [i] | ||
| 28 | No linear OOA(461, 40, F4, 2, 53) (dual of [(40, 2), 19, 54]-NRT-code) | [i] | ||
| 29 | No linear OOA(462, 40, F4, 2, 54) (dual of [(40, 2), 18, 55]-NRT-code) | [i] | ||
| 30 | No linear OOA(463, 40, F4, 2, 55) (dual of [(40, 2), 17, 56]-NRT-code) | [i] | ||
| 31 | No linear OOA(464, 40, F4, 2, 56) (dual of [(40, 2), 16, 57]-NRT-code) | [i] | ||
| 32 | No linear OOA(465, 40, F4, 2, 57) (dual of [(40, 2), 15, 58]-NRT-code) | [i] | ||
| 33 | No linear OOA(466, 40, F4, 2, 58) (dual of [(40, 2), 14, 59]-NRT-code) | [i] | ||
| 34 | No linear OOA(467, 40, F4, 2, 59) (dual of [(40, 2), 13, 60]-NRT-code) | [i] | ||
| 35 | No linear OOA(436, 40, F4, 2, 28) (dual of [(40, 2), 44, 29]-NRT-code) | [i] | Depth Reduction | |
| 36 | No linear OOA(436, 40, F4, 3, 28) (dual of [(40, 3), 84, 29]-NRT-code) | [i] | ||
| 37 | No digital (8, 36, 40)-net over F4 | [i] | Extracting Embedded Orthogonal Array | |
| 38 | No linear OA(4148, 153, F4, 112) (dual of [153, 5, 113]-code) | [i] | Residual Code | |
| 39 | No linear OA(437, 46, F4, 28) (dual of [46, 9, 29]-code) | [i] | Construction Y1 (Bound) | |