Information on Result #547938
There is no linear OA(550, 59, F5, 40) (dual of [59, 9, 41]-code), because construction Y1 would yield
- linear OA(549, 53, F5, 40) (dual of [53, 4, 41]-code), but
- residual code [i] would yield linear OA(59, 12, F5, 8) (dual of [12, 3, 9]-code), but
- OA(59, 59, S5, 6), but
- discarding factors would yield OA(59, 58, S5, 6), but
- the Rao or (dual) Hamming bound shows that M ≥ 2 001465 > 59 [i]
- discarding factors would yield OA(59, 58, S5, 6), 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(551, 60, F5, 41) (dual of [60, 9, 42]-code) | [i] | Truncation | |
| 2 | No linear OOA(551, 59, F5, 2, 41) (dual of [(59, 2), 67, 42]-NRT-code) | [i] | m-Reduction for OOAs | |
| 3 | No linear OOA(552, 59, F5, 2, 42) (dual of [(59, 2), 66, 43]-NRT-code) | [i] | ||
| 4 | No linear OOA(553, 59, F5, 2, 43) (dual of [(59, 2), 65, 44]-NRT-code) | [i] | ||
| 5 | No linear OOA(554, 59, F5, 2, 44) (dual of [(59, 2), 64, 45]-NRT-code) | [i] | ||
| 6 | No linear OOA(556, 59, F5, 2, 46) (dual of [(59, 2), 62, 47]-NRT-code) | [i] | ||
| 7 | No linear OOA(557, 59, F5, 2, 47) (dual of [(59, 2), 61, 48]-NRT-code) | [i] | ||
| 8 | No linear OOA(558, 59, F5, 2, 48) (dual of [(59, 2), 60, 49]-NRT-code) | [i] | ||
| 9 | No linear OOA(559, 59, F5, 2, 49) (dual of [(59, 2), 59, 50]-NRT-code) | [i] | ||
| 10 | No linear OOA(560, 59, F5, 2, 50) (dual of [(59, 2), 58, 51]-NRT-code) | [i] | ||
| 11 | No linear OOA(561, 59, F5, 2, 51) (dual of [(59, 2), 57, 52]-NRT-code) | [i] | ||
| 12 | No linear OOA(562, 59, F5, 2, 52) (dual of [(59, 2), 56, 53]-NRT-code) | [i] | ||
| 13 | No linear OOA(563, 59, F5, 2, 53) (dual of [(59, 2), 55, 54]-NRT-code) | [i] | ||
| 14 | No linear OOA(564, 59, F5, 2, 54) (dual of [(59, 2), 54, 55]-NRT-code) | [i] | ||
| 15 | No linear OOA(565, 59, F5, 2, 55) (dual of [(59, 2), 53, 56]-NRT-code) | [i] | ||
| 16 | No linear OOA(566, 59, F5, 2, 56) (dual of [(59, 2), 52, 57]-NRT-code) | [i] | ||
| 17 | No linear OOA(567, 59, F5, 2, 57) (dual of [(59, 2), 51, 58]-NRT-code) | [i] | ||
| 18 | No linear OOA(568, 59, F5, 2, 58) (dual of [(59, 2), 50, 59]-NRT-code) | [i] | ||
| 19 | No linear OOA(569, 59, F5, 2, 59) (dual of [(59, 2), 49, 60]-NRT-code) | [i] | ||
| 20 | No linear OOA(570, 59, F5, 2, 60) (dual of [(59, 2), 48, 61]-NRT-code) | [i] | ||
| 21 | No linear OOA(571, 59, F5, 2, 61) (dual of [(59, 2), 47, 62]-NRT-code) | [i] | ||
| 22 | No linear OOA(572, 59, F5, 2, 62) (dual of [(59, 2), 46, 63]-NRT-code) | [i] | ||
| 23 | No linear OOA(573, 59, F5, 2, 63) (dual of [(59, 2), 45, 64]-NRT-code) | [i] | ||
| 24 | No linear OOA(574, 59, F5, 2, 64) (dual of [(59, 2), 44, 65]-NRT-code) | [i] | ||
| 25 | No linear OOA(575, 59, F5, 2, 65) (dual of [(59, 2), 43, 66]-NRT-code) | [i] | ||
| 26 | No linear OOA(576, 59, F5, 2, 66) (dual of [(59, 2), 42, 67]-NRT-code) | [i] | ||
| 27 | No linear OOA(577, 59, F5, 2, 67) (dual of [(59, 2), 41, 68]-NRT-code) | [i] | ||
| 28 | No linear OOA(578, 59, F5, 2, 68) (dual of [(59, 2), 40, 69]-NRT-code) | [i] | ||
| 29 | No linear OOA(579, 59, F5, 2, 69) (dual of [(59, 2), 39, 70]-NRT-code) | [i] | ||
| 30 | No linear OOA(580, 59, F5, 2, 70) (dual of [(59, 2), 38, 71]-NRT-code) | [i] | ||
| 31 | No linear OOA(581, 59, F5, 2, 71) (dual of [(59, 2), 37, 72]-NRT-code) | [i] | ||
| 32 | No linear OOA(582, 59, F5, 2, 72) (dual of [(59, 2), 36, 73]-NRT-code) | [i] | ||
| 33 | No linear OOA(583, 59, F5, 2, 73) (dual of [(59, 2), 35, 74]-NRT-code) | [i] | ||
| 34 | No linear OOA(584, 59, F5, 2, 74) (dual of [(59, 2), 34, 75]-NRT-code) | [i] | ||
| 35 | No linear OOA(585, 59, F5, 2, 75) (dual of [(59, 2), 33, 76]-NRT-code) | [i] | ||
| 36 | No linear OOA(586, 59, F5, 2, 76) (dual of [(59, 2), 32, 77]-NRT-code) | [i] | ||
| 37 | No linear OOA(587, 59, F5, 2, 77) (dual of [(59, 2), 31, 78]-NRT-code) | [i] | ||
| 38 | No linear OOA(588, 59, F5, 2, 78) (dual of [(59, 2), 30, 79]-NRT-code) | [i] | ||
| 39 | No linear OOA(589, 59, F5, 2, 79) (dual of [(59, 2), 29, 80]-NRT-code) | [i] | ||
| 40 | No linear OOA(590, 59, F5, 2, 80) (dual of [(59, 2), 28, 81]-NRT-code) | [i] | ||
| 41 | No linear OOA(591, 59, F5, 2, 81) (dual of [(59, 2), 27, 82]-NRT-code) | [i] | ||
| 42 | No linear OOA(592, 59, F5, 2, 82) (dual of [(59, 2), 26, 83]-NRT-code) | [i] | ||
| 43 | No linear OOA(593, 59, F5, 2, 83) (dual of [(59, 2), 25, 84]-NRT-code) | [i] | ||
| 44 | No linear OOA(594, 59, F5, 2, 84) (dual of [(59, 2), 24, 85]-NRT-code) | [i] | ||
| 45 | No linear OOA(595, 59, F5, 2, 85) (dual of [(59, 2), 23, 86]-NRT-code) | [i] | ||
| 46 | No linear OOA(596, 59, F5, 2, 86) (dual of [(59, 2), 22, 87]-NRT-code) | [i] | ||
| 47 | No linear OOA(597, 59, F5, 2, 87) (dual of [(59, 2), 21, 88]-NRT-code) | [i] | ||
| 48 | No linear OOA(598, 59, F5, 2, 88) (dual of [(59, 2), 20, 89]-NRT-code) | [i] | ||
| 49 | No linear OOA(599, 59, F5, 2, 89) (dual of [(59, 2), 19, 90]-NRT-code) | [i] | ||
| 50 | No linear OOA(5100, 59, F5, 2, 90) (dual of [(59, 2), 18, 91]-NRT-code) | [i] | ||
| 51 | No linear OOA(5101, 59, F5, 2, 91) (dual of [(59, 2), 17, 92]-NRT-code) | [i] | ||
| 52 | No linear OOA(5102, 59, F5, 2, 92) (dual of [(59, 2), 16, 93]-NRT-code) | [i] | ||
| 53 | No linear OOA(5103, 59, F5, 2, 93) (dual of [(59, 2), 15, 94]-NRT-code) | [i] | ||
| 54 | No linear OOA(5104, 59, F5, 2, 94) (dual of [(59, 2), 14, 95]-NRT-code) | [i] | ||
| 55 | No linear OOA(550, 59, F5, 2, 40) (dual of [(59, 2), 68, 41]-NRT-code) | [i] | Depth Reduction | |
| 56 | No linear OOA(550, 59, F5, 3, 40) (dual of [(59, 3), 127, 41]-NRT-code) | [i] | ||
| 57 | No digital (10, 50, 59)-net over F5 | [i] | Extracting Embedded Orthogonal Array | |