Information on Result #547934
There is no linear OA(531, 39, F5, 25) (dual of [39, 8, 26]-code), because construction Y1 would yield
- linear OA(530, 33, F5, 25) (dual of [33, 3, 26]-code), but
- OA(58, 39, S5, 6), but
- discarding factors would yield OA(58, 34, S5, 6), but
- the Rao or (dual) Hamming bound shows that M ≥ 392089 > 58 [i]
- discarding factors would yield OA(58, 34, 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(532, 40, F5, 26) (dual of [40, 8, 27]-code) | [i] | Truncation | |
| 2 | No linear OA(533, 41, F5, 27) (dual of [41, 8, 28]-code) | [i] | ||
| 3 | No linear OOA(532, 39, F5, 2, 26) (dual of [(39, 2), 46, 27]-NRT-code) | [i] | m-Reduction for OOAs | |
| 4 | No linear OOA(533, 39, F5, 2, 27) (dual of [(39, 2), 45, 28]-NRT-code) | [i] | ||
| 5 | No linear OOA(534, 39, F5, 2, 28) (dual of [(39, 2), 44, 29]-NRT-code) | [i] | ||
| 6 | No linear OOA(535, 39, F5, 2, 29) (dual of [(39, 2), 43, 30]-NRT-code) | [i] | ||
| 7 | No linear OOA(537, 39, F5, 2, 31) (dual of [(39, 2), 41, 32]-NRT-code) | [i] | ||
| 8 | No linear OOA(538, 39, F5, 2, 32) (dual of [(39, 2), 40, 33]-NRT-code) | [i] | ||
| 9 | No linear OOA(539, 39, F5, 2, 33) (dual of [(39, 2), 39, 34]-NRT-code) | [i] | ||
| 10 | No linear OOA(540, 39, F5, 2, 34) (dual of [(39, 2), 38, 35]-NRT-code) | [i] | ||
| 11 | No linear OOA(541, 39, F5, 2, 35) (dual of [(39, 2), 37, 36]-NRT-code) | [i] | ||
| 12 | No linear OOA(542, 39, F5, 2, 36) (dual of [(39, 2), 36, 37]-NRT-code) | [i] | ||
| 13 | No linear OOA(543, 39, F5, 2, 37) (dual of [(39, 2), 35, 38]-NRT-code) | [i] | ||
| 14 | No linear OOA(544, 39, F5, 2, 38) (dual of [(39, 2), 34, 39]-NRT-code) | [i] | ||
| 15 | No linear OOA(545, 39, F5, 2, 39) (dual of [(39, 2), 33, 40]-NRT-code) | [i] | ||
| 16 | No linear OOA(546, 39, F5, 2, 40) (dual of [(39, 2), 32, 41]-NRT-code) | [i] | ||
| 17 | No linear OOA(547, 39, F5, 2, 41) (dual of [(39, 2), 31, 42]-NRT-code) | [i] | ||
| 18 | No linear OOA(548, 39, F5, 2, 42) (dual of [(39, 2), 30, 43]-NRT-code) | [i] | ||
| 19 | No linear OOA(549, 39, F5, 2, 43) (dual of [(39, 2), 29, 44]-NRT-code) | [i] | ||
| 20 | No linear OOA(550, 39, F5, 2, 44) (dual of [(39, 2), 28, 45]-NRT-code) | [i] | ||
| 21 | No linear OOA(551, 39, F5, 2, 45) (dual of [(39, 2), 27, 46]-NRT-code) | [i] | ||
| 22 | No linear OOA(552, 39, F5, 2, 46) (dual of [(39, 2), 26, 47]-NRT-code) | [i] | ||
| 23 | No linear OOA(553, 39, F5, 2, 47) (dual of [(39, 2), 25, 48]-NRT-code) | [i] | ||
| 24 | No linear OOA(554, 39, F5, 2, 48) (dual of [(39, 2), 24, 49]-NRT-code) | [i] | ||
| 25 | No linear OOA(555, 39, F5, 2, 49) (dual of [(39, 2), 23, 50]-NRT-code) | [i] | ||
| 26 | No linear OOA(556, 39, F5, 2, 50) (dual of [(39, 2), 22, 51]-NRT-code) | [i] | ||
| 27 | No linear OOA(557, 39, F5, 2, 51) (dual of [(39, 2), 21, 52]-NRT-code) | [i] | ||
| 28 | No linear OOA(558, 39, F5, 2, 52) (dual of [(39, 2), 20, 53]-NRT-code) | [i] | ||
| 29 | No linear OOA(559, 39, F5, 2, 53) (dual of [(39, 2), 19, 54]-NRT-code) | [i] | ||
| 30 | No linear OOA(560, 39, F5, 2, 54) (dual of [(39, 2), 18, 55]-NRT-code) | [i] | ||
| 31 | No linear OOA(561, 39, F5, 2, 55) (dual of [(39, 2), 17, 56]-NRT-code) | [i] | ||
| 32 | No linear OOA(562, 39, F5, 2, 56) (dual of [(39, 2), 16, 57]-NRT-code) | [i] | ||
| 33 | No linear OOA(563, 39, F5, 2, 57) (dual of [(39, 2), 15, 58]-NRT-code) | [i] | ||
| 34 | No linear OOA(564, 39, F5, 2, 58) (dual of [(39, 2), 14, 59]-NRT-code) | [i] | ||
| 35 | No linear OOA(565, 39, F5, 2, 59) (dual of [(39, 2), 13, 60]-NRT-code) | [i] | ||
| 36 | No linear OOA(566, 39, F5, 2, 60) (dual of [(39, 2), 12, 61]-NRT-code) | [i] | ||
| 37 | No linear OOA(567, 39, F5, 2, 61) (dual of [(39, 2), 11, 62]-NRT-code) | [i] | ||
| 38 | No linear OOA(568, 39, F5, 2, 62) (dual of [(39, 2), 10, 63]-NRT-code) | [i] | ||
| 39 | No linear OOA(531, 39, F5, 2, 25) (dual of [(39, 2), 47, 26]-NRT-code) | [i] | Depth Reduction | |
| 40 | No linear OOA(531, 39, F5, 3, 25) (dual of [(39, 3), 86, 26]-NRT-code) | [i] | ||
| 41 | No digital (6, 31, 39)-net over F5 | [i] | Extracting Embedded Orthogonal Array | |
| 42 | No linear OA(532, 66, F5, 25) (dual of [66, 34, 26]-code) | [i] | Construction Y1 (Bound) | |