Information on Result #547516
There is no linear OA(537, 43, F5, 30) (dual of [43, 6, 31]-code), because residual code would yield linear OA(57, 12, F5, 6) (dual of [12, 5, 7]-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(538, 44, F5, 31) (dual of [44, 6, 32]-code) | [i] | Truncation | |
| 2 | No linear OA(539, 45, F5, 32) (dual of [45, 6, 33]-code) | [i] | ||
| 3 | No linear OOA(538, 43, F5, 2, 31) (dual of [(43, 2), 48, 32]-NRT-code) | [i] | m-Reduction for OOAs | |
| 4 | No linear OOA(539, 43, F5, 2, 32) (dual of [(43, 2), 47, 33]-NRT-code) | [i] | ||
| 5 | No linear OOA(540, 43, F5, 2, 33) (dual of [(43, 2), 46, 34]-NRT-code) | [i] | ||
| 6 | No linear OOA(541, 43, F5, 2, 34) (dual of [(43, 2), 45, 35]-NRT-code) | [i] | ||
| 7 | No linear OOA(542, 43, F5, 2, 35) (dual of [(43, 2), 44, 36]-NRT-code) | [i] | ||
| 8 | No linear OOA(543, 43, F5, 2, 36) (dual of [(43, 2), 43, 37]-NRT-code) | [i] | ||
| 9 | No linear OOA(544, 43, F5, 2, 37) (dual of [(43, 2), 42, 38]-NRT-code) | [i] | ||
| 10 | No linear OOA(545, 43, F5, 2, 38) (dual of [(43, 2), 41, 39]-NRT-code) | [i] | ||
| 11 | No linear OOA(546, 43, F5, 2, 39) (dual of [(43, 2), 40, 40]-NRT-code) | [i] | ||
| 12 | No linear OOA(547, 43, F5, 2, 40) (dual of [(43, 2), 39, 41]-NRT-code) | [i] | ||
| 13 | No linear OOA(548, 43, F5, 2, 41) (dual of [(43, 2), 38, 42]-NRT-code) | [i] | ||
| 14 | No linear OOA(549, 43, F5, 2, 42) (dual of [(43, 2), 37, 43]-NRT-code) | [i] | ||
| 15 | No linear OOA(550, 43, F5, 2, 43) (dual of [(43, 2), 36, 44]-NRT-code) | [i] | ||
| 16 | No linear OOA(551, 43, F5, 2, 44) (dual of [(43, 2), 35, 45]-NRT-code) | [i] | ||
| 17 | No linear OOA(552, 43, F5, 2, 45) (dual of [(43, 2), 34, 46]-NRT-code) | [i] | ||
| 18 | No linear OOA(553, 43, F5, 2, 46) (dual of [(43, 2), 33, 47]-NRT-code) | [i] | ||
| 19 | No linear OOA(554, 43, F5, 2, 47) (dual of [(43, 2), 32, 48]-NRT-code) | [i] | ||
| 20 | No linear OOA(555, 43, F5, 2, 48) (dual of [(43, 2), 31, 49]-NRT-code) | [i] | ||
| 21 | No linear OOA(556, 43, F5, 2, 49) (dual of [(43, 2), 30, 50]-NRT-code) | [i] | ||
| 22 | No linear OOA(557, 43, F5, 2, 50) (dual of [(43, 2), 29, 51]-NRT-code) | [i] | ||
| 23 | No linear OOA(558, 43, F5, 2, 51) (dual of [(43, 2), 28, 52]-NRT-code) | [i] | ||
| 24 | No linear OOA(559, 43, F5, 2, 52) (dual of [(43, 2), 27, 53]-NRT-code) | [i] | ||
| 25 | No linear OOA(560, 43, F5, 2, 53) (dual of [(43, 2), 26, 54]-NRT-code) | [i] | ||
| 26 | No linear OOA(561, 43, F5, 2, 54) (dual of [(43, 2), 25, 55]-NRT-code) | [i] | ||
| 27 | No linear OOA(562, 43, F5, 2, 55) (dual of [(43, 2), 24, 56]-NRT-code) | [i] | ||
| 28 | No linear OOA(563, 43, F5, 2, 56) (dual of [(43, 2), 23, 57]-NRT-code) | [i] | ||
| 29 | No linear OOA(564, 43, F5, 2, 57) (dual of [(43, 2), 22, 58]-NRT-code) | [i] | ||
| 30 | No linear OOA(565, 43, F5, 2, 58) (dual of [(43, 2), 21, 59]-NRT-code) | [i] | ||
| 31 | No linear OOA(566, 43, F5, 2, 59) (dual of [(43, 2), 20, 60]-NRT-code) | [i] | ||
| 32 | No linear OOA(567, 43, F5, 2, 60) (dual of [(43, 2), 19, 61]-NRT-code) | [i] | ||
| 33 | No linear OOA(568, 43, F5, 2, 61) (dual of [(43, 2), 18, 62]-NRT-code) | [i] | ||
| 34 | No linear OOA(569, 43, F5, 2, 62) (dual of [(43, 2), 17, 63]-NRT-code) | [i] | ||
| 35 | No linear OOA(570, 43, F5, 2, 63) (dual of [(43, 2), 16, 64]-NRT-code) | [i] | ||
| 36 | No linear OOA(571, 43, F5, 2, 64) (dual of [(43, 2), 15, 65]-NRT-code) | [i] | ||
| 37 | No linear OOA(572, 43, F5, 2, 65) (dual of [(43, 2), 14, 66]-NRT-code) | [i] | ||
| 38 | No linear OOA(573, 43, F5, 2, 66) (dual of [(43, 2), 13, 67]-NRT-code) | [i] | ||
| 39 | No linear OOA(574, 43, F5, 2, 67) (dual of [(43, 2), 12, 68]-NRT-code) | [i] | ||
| 40 | No linear OOA(575, 43, F5, 2, 68) (dual of [(43, 2), 11, 69]-NRT-code) | [i] | ||
| 41 | No linear OOA(576, 43, F5, 2, 69) (dual of [(43, 2), 10, 70]-NRT-code) | [i] | ||
| 42 | No linear OOA(537, 43, F5, 2, 30) (dual of [(43, 2), 49, 31]-NRT-code) | [i] | Depth Reduction | |
| 43 | No linear OOA(537, 43, F5, 3, 30) (dual of [(43, 3), 92, 31]-NRT-code) | [i] | ||
| 44 | No digital (7, 37, 43)-net over F5 | [i] | Extracting Embedded Orthogonal Array | |
| 45 | No linear OA(538, 61, F5, 30) (dual of [61, 23, 31]-code) | [i] | Construction Y1 (Bound) | |
| 46 | No linear OA(56, 43, F5, 4) (dual of [43, 37, 5]-code) | [i] | ||