Information on Result #547520
There is no linear OA(549, 53, F5, 40) (dual of [53, 4, 41]-code), because residual code would yield linear OA(59, 12, F5, 8) (dual of [12, 3, 9]-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(550, 54, F5, 41) (dual of [54, 4, 42]-code) | [i] | Truncation | |
| 2 | No linear OA(551, 55, F5, 42) (dual of [55, 4, 43]-code) | [i] | ||
| 3 | No linear OA(552, 56, F5, 43) (dual of [56, 4, 44]-code) | [i] | ||
| 4 | No linear OA(553, 57, F5, 44) (dual of [57, 4, 45]-code) | [i] | ||
| 5 | No linear OOA(550, 53, F5, 2, 41) (dual of [(53, 2), 56, 42]-NRT-code) | [i] | m-Reduction for OOAs | |
| 6 | No linear OOA(551, 53, F5, 2, 42) (dual of [(53, 2), 55, 43]-NRT-code) | [i] | ||
| 7 | No linear OOA(552, 53, F5, 2, 43) (dual of [(53, 2), 54, 44]-NRT-code) | [i] | ||
| 8 | No linear OOA(553, 53, F5, 2, 44) (dual of [(53, 2), 53, 45]-NRT-code) | [i] | ||
| 9 | No linear OOA(554, 53, F5, 2, 45) (dual of [(53, 2), 52, 46]-NRT-code) | [i] | ||
| 10 | No linear OOA(555, 53, F5, 2, 46) (dual of [(53, 2), 51, 47]-NRT-code) | [i] | ||
| 11 | No linear OOA(556, 53, F5, 2, 47) (dual of [(53, 2), 50, 48]-NRT-code) | [i] | ||
| 12 | No linear OOA(557, 53, F5, 2, 48) (dual of [(53, 2), 49, 49]-NRT-code) | [i] | ||
| 13 | No linear OOA(558, 53, F5, 2, 49) (dual of [(53, 2), 48, 50]-NRT-code) | [i] | ||
| 14 | No linear OOA(559, 53, F5, 2, 50) (dual of [(53, 2), 47, 51]-NRT-code) | [i] | ||
| 15 | No linear OOA(560, 53, F5, 2, 51) (dual of [(53, 2), 46, 52]-NRT-code) | [i] | ||
| 16 | No linear OOA(561, 53, F5, 2, 52) (dual of [(53, 2), 45, 53]-NRT-code) | [i] | ||
| 17 | No linear OOA(562, 53, F5, 2, 53) (dual of [(53, 2), 44, 54]-NRT-code) | [i] | ||
| 18 | No linear OOA(563, 53, F5, 2, 54) (dual of [(53, 2), 43, 55]-NRT-code) | [i] | ||
| 19 | No linear OOA(564, 53, F5, 2, 55) (dual of [(53, 2), 42, 56]-NRT-code) | [i] | ||
| 20 | No linear OOA(565, 53, F5, 2, 56) (dual of [(53, 2), 41, 57]-NRT-code) | [i] | ||
| 21 | No linear OOA(566, 53, F5, 2, 57) (dual of [(53, 2), 40, 58]-NRT-code) | [i] | ||
| 22 | No linear OOA(567, 53, F5, 2, 58) (dual of [(53, 2), 39, 59]-NRT-code) | [i] | ||
| 23 | No linear OOA(568, 53, F5, 2, 59) (dual of [(53, 2), 38, 60]-NRT-code) | [i] | ||
| 24 | No linear OOA(569, 53, F5, 2, 60) (dual of [(53, 2), 37, 61]-NRT-code) | [i] | ||
| 25 | No linear OOA(570, 53, F5, 2, 61) (dual of [(53, 2), 36, 62]-NRT-code) | [i] | ||
| 26 | No linear OOA(571, 53, F5, 2, 62) (dual of [(53, 2), 35, 63]-NRT-code) | [i] | ||
| 27 | No linear OOA(572, 53, F5, 2, 63) (dual of [(53, 2), 34, 64]-NRT-code) | [i] | ||
| 28 | No linear OOA(573, 53, F5, 2, 64) (dual of [(53, 2), 33, 65]-NRT-code) | [i] | ||
| 29 | No linear OOA(574, 53, F5, 2, 65) (dual of [(53, 2), 32, 66]-NRT-code) | [i] | ||
| 30 | No linear OOA(575, 53, F5, 2, 66) (dual of [(53, 2), 31, 67]-NRT-code) | [i] | ||
| 31 | No linear OOA(576, 53, F5, 2, 67) (dual of [(53, 2), 30, 68]-NRT-code) | [i] | ||
| 32 | No linear OOA(577, 53, F5, 2, 68) (dual of [(53, 2), 29, 69]-NRT-code) | [i] | ||
| 33 | No linear OOA(578, 53, F5, 2, 69) (dual of [(53, 2), 28, 70]-NRT-code) | [i] | ||
| 34 | No linear OOA(579, 53, F5, 2, 70) (dual of [(53, 2), 27, 71]-NRT-code) | [i] | ||
| 35 | No linear OOA(580, 53, F5, 2, 71) (dual of [(53, 2), 26, 72]-NRT-code) | [i] | ||
| 36 | No linear OOA(581, 53, F5, 2, 72) (dual of [(53, 2), 25, 73]-NRT-code) | [i] | ||
| 37 | No linear OOA(582, 53, F5, 2, 73) (dual of [(53, 2), 24, 74]-NRT-code) | [i] | ||
| 38 | No linear OOA(583, 53, F5, 2, 74) (dual of [(53, 2), 23, 75]-NRT-code) | [i] | ||
| 39 | No linear OOA(584, 53, F5, 2, 75) (dual of [(53, 2), 22, 76]-NRT-code) | [i] | ||
| 40 | No linear OOA(585, 53, F5, 2, 76) (dual of [(53, 2), 21, 77]-NRT-code) | [i] | ||
| 41 | No linear OOA(586, 53, F5, 2, 77) (dual of [(53, 2), 20, 78]-NRT-code) | [i] | ||
| 42 | No linear OOA(587, 53, F5, 2, 78) (dual of [(53, 2), 19, 79]-NRT-code) | [i] | ||
| 43 | No linear OOA(588, 53, F5, 2, 79) (dual of [(53, 2), 18, 80]-NRT-code) | [i] | ||
| 44 | No linear OOA(589, 53, F5, 2, 80) (dual of [(53, 2), 17, 81]-NRT-code) | [i] | ||
| 45 | No linear OOA(590, 53, F5, 2, 81) (dual of [(53, 2), 16, 82]-NRT-code) | [i] | ||
| 46 | No linear OOA(591, 53, F5, 2, 82) (dual of [(53, 2), 15, 83]-NRT-code) | [i] | ||
| 47 | No linear OOA(592, 53, F5, 2, 83) (dual of [(53, 2), 14, 84]-NRT-code) | [i] | ||
| 48 | No linear OOA(593, 53, F5, 2, 84) (dual of [(53, 2), 13, 85]-NRT-code) | [i] | ||
| 49 | No linear OOA(594, 53, F5, 2, 85) (dual of [(53, 2), 12, 86]-NRT-code) | [i] | ||
| 50 | No linear OOA(549, 53, F5, 2, 40) (dual of [(53, 2), 57, 41]-NRT-code) | [i] | Depth Reduction | |
| 51 | No linear OOA(549, 53, F5, 3, 40) (dual of [(53, 3), 110, 41]-NRT-code) | [i] | ||
| 52 | No digital (9, 49, 53)-net over F5 | [i] | Extracting Embedded Orthogonal Array | |
| 53 | No linear OA(550, 59, F5, 40) (dual of [59, 9, 41]-code) | [i] | Construction Y1 (Bound) | |