Information on Result #546144
There is no linear OA(452, 56, F4, 40) (dual of [56, 4, 41]-code), because improvement by Maruta on the Griesmer bound
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
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | No linear OA(453, 57, F4, 41) (dual of [57, 4, 42]-code) | [i] | Truncation | |
| 2 | No linear OA(454, 58, F4, 42) (dual of [58, 4, 43]-code) | [i] | ||
| 3 | No linear OA(455, 59, F4, 43) (dual of [59, 4, 44]-code) | [i] | ||
| 4 | No linear OOA(453, 56, F4, 2, 41) (dual of [(56, 2), 59, 42]-NRT-code) | [i] | m-Reduction for OOAs | |
| 5 | No linear OOA(454, 56, F4, 2, 42) (dual of [(56, 2), 58, 43]-NRT-code) | [i] | ||
| 6 | No linear OOA(455, 56, F4, 2, 43) (dual of [(56, 2), 57, 44]-NRT-code) | [i] | ||
| 7 | No linear OOA(456, 56, F4, 2, 44) (dual of [(56, 2), 56, 45]-NRT-code) | [i] | ||
| 8 | No linear OOA(457, 56, F4, 2, 45) (dual of [(56, 2), 55, 46]-NRT-code) | [i] | ||
| 9 | No linear OOA(458, 56, F4, 2, 46) (dual of [(56, 2), 54, 47]-NRT-code) | [i] | ||
| 10 | No linear OOA(459, 56, F4, 2, 47) (dual of [(56, 2), 53, 48]-NRT-code) | [i] | ||
| 11 | No linear OOA(460, 56, F4, 2, 48) (dual of [(56, 2), 52, 49]-NRT-code) | [i] | ||
| 12 | No linear OOA(461, 56, F4, 2, 49) (dual of [(56, 2), 51, 50]-NRT-code) | [i] | ||
| 13 | No linear OOA(462, 56, F4, 2, 50) (dual of [(56, 2), 50, 51]-NRT-code) | [i] | ||
| 14 | No linear OOA(463, 56, F4, 2, 51) (dual of [(56, 2), 49, 52]-NRT-code) | [i] | ||
| 15 | No linear OOA(464, 56, F4, 2, 52) (dual of [(56, 2), 48, 53]-NRT-code) | [i] | ||
| 16 | No linear OOA(465, 56, F4, 2, 53) (dual of [(56, 2), 47, 54]-NRT-code) | [i] | ||
| 17 | No linear OOA(466, 56, F4, 2, 54) (dual of [(56, 2), 46, 55]-NRT-code) | [i] | ||
| 18 | No linear OOA(467, 56, F4, 2, 55) (dual of [(56, 2), 45, 56]-NRT-code) | [i] | ||
| 19 | No linear OOA(468, 56, F4, 2, 56) (dual of [(56, 2), 44, 57]-NRT-code) | [i] | ||
| 20 | No linear OOA(469, 56, F4, 2, 57) (dual of [(56, 2), 43, 58]-NRT-code) | [i] | ||
| 21 | No linear OOA(470, 56, F4, 2, 58) (dual of [(56, 2), 42, 59]-NRT-code) | [i] | ||
| 22 | No linear OOA(471, 56, F4, 2, 59) (dual of [(56, 2), 41, 60]-NRT-code) | [i] | ||
| 23 | No linear OOA(472, 56, F4, 2, 60) (dual of [(56, 2), 40, 61]-NRT-code) | [i] | ||
| 24 | No linear OOA(473, 56, F4, 2, 61) (dual of [(56, 2), 39, 62]-NRT-code) | [i] | ||
| 25 | No linear OOA(474, 56, F4, 2, 62) (dual of [(56, 2), 38, 63]-NRT-code) | [i] | ||
| 26 | No linear OOA(475, 56, F4, 2, 63) (dual of [(56, 2), 37, 64]-NRT-code) | [i] | ||
| 27 | No linear OOA(476, 56, F4, 2, 64) (dual of [(56, 2), 36, 65]-NRT-code) | [i] | ||
| 28 | No linear OOA(477, 56, F4, 2, 65) (dual of [(56, 2), 35, 66]-NRT-code) | [i] | ||
| 29 | No linear OOA(478, 56, F4, 2, 66) (dual of [(56, 2), 34, 67]-NRT-code) | [i] | ||
| 30 | No linear OOA(479, 56, F4, 2, 67) (dual of [(56, 2), 33, 68]-NRT-code) | [i] | ||
| 31 | No linear OOA(480, 56, F4, 2, 68) (dual of [(56, 2), 32, 69]-NRT-code) | [i] | ||
| 32 | No linear OOA(481, 56, F4, 2, 69) (dual of [(56, 2), 31, 70]-NRT-code) | [i] | ||
| 33 | No linear OOA(482, 56, F4, 2, 70) (dual of [(56, 2), 30, 71]-NRT-code) | [i] | ||
| 34 | No linear OOA(483, 56, F4, 2, 71) (dual of [(56, 2), 29, 72]-NRT-code) | [i] | ||
| 35 | No linear OOA(484, 56, F4, 2, 72) (dual of [(56, 2), 28, 73]-NRT-code) | [i] | ||
| 36 | No linear OOA(485, 56, F4, 2, 73) (dual of [(56, 2), 27, 74]-NRT-code) | [i] | ||
| 37 | No linear OOA(486, 56, F4, 2, 74) (dual of [(56, 2), 26, 75]-NRT-code) | [i] | ||
| 38 | No linear OOA(487, 56, F4, 2, 75) (dual of [(56, 2), 25, 76]-NRT-code) | [i] | ||
| 39 | No linear OOA(488, 56, F4, 2, 76) (dual of [(56, 2), 24, 77]-NRT-code) | [i] | ||
| 40 | No linear OOA(489, 56, F4, 2, 77) (dual of [(56, 2), 23, 78]-NRT-code) | [i] | ||
| 41 | No linear OOA(490, 56, F4, 2, 78) (dual of [(56, 2), 22, 79]-NRT-code) | [i] | ||
| 42 | No linear OOA(491, 56, F4, 2, 79) (dual of [(56, 2), 21, 80]-NRT-code) | [i] | ||
| 43 | No linear OOA(492, 56, F4, 2, 80) (dual of [(56, 2), 20, 81]-NRT-code) | [i] | ||
| 44 | No linear OOA(493, 56, F4, 2, 81) (dual of [(56, 2), 19, 82]-NRT-code) | [i] | ||
| 45 | No linear OOA(494, 56, F4, 2, 82) (dual of [(56, 2), 18, 83]-NRT-code) | [i] | ||
| 46 | No linear OOA(452, 56, F4, 2, 40) (dual of [(56, 2), 60, 41]-NRT-code) | [i] | Depth Reduction | |
| 47 | No linear OOA(452, 56, F4, 3, 40) (dual of [(56, 3), 116, 41]-NRT-code) | [i] | ||
| 48 | No digital (12, 52, 56)-net over F4 | [i] | Extracting Embedded Orthogonal Array | |
| 49 | No linear OA(4212, 217, F4, 160) (dual of [217, 5, 161]-code) | [i] | Residual Code | |
| 50 | No linear OA(453, 60, F4, 40) (dual of [60, 7, 41]-code) | [i] | Construction Y1 (Bound) | |