Information on Result #613759
Linear OA(585, 15625, F5, 18) (dual of [15625, 15540, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18
Mode: Constructive and 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.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OA(594, 15635, F5, 18) (dual of [15635, 15541, 19]-code) | [i] | (u, u+v)-Construction | |
| 2 | Linear OA(595, 15637, F5, 18) (dual of [15637, 15542, 19]-code) | [i] | ||
| 3 | Linear OA(596, 15639, F5, 18) (dual of [15639, 15543, 19]-code) | [i] | ||
| 4 | Linear OA(597, 15641, F5, 18) (dual of [15641, 15544, 19]-code) | [i] | ||
| 5 | Linear OA(598, 15653, F5, 18) (dual of [15653, 15555, 19]-code) | [i] | ||
| 6 | Linear OOA(585, 7934, F5, 2, 18) (dual of [(7934, 2), 15783, 19]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 7 | Linear OOA(585, 7934, F5, 3, 18) (dual of [(7934, 3), 23717, 19]-NRT-code) | [i] | ||
| 8 | Digital (67, 85, 7934)-net over F5 | [i] | ||
| 9 | Linear OA(598, 15639, F5, 18) (dual of [15639, 15541, 19]-code) | [i] | (u, u−v, u+v+w)-Construction | |
| 10 | Linear OA(591, 15631, F5, 19) (dual of [15631, 15540, 20]-code) | [i] | ✔ | Construction X with Extended Narrow-Sense BCH Codes |
| 11 | Linear OA(585, 15631, F5, 18) (dual of [15631, 15546, 19]-code) | [i] | ✔ | |
| 12 | Linear OA(598, 15638, F5, 20) (dual of [15638, 15540, 21]-code) | [i] | ✔ | |
| 13 | Linear OA(5100, 15640, F5, 21) (dual of [15640, 15540, 22]-code) | [i] | ✔ | |
| 14 | Linear OA(586, 15638, F5, 18) (dual of [15638, 15552, 19]-code) | [i] | ✔ | |
| 15 | Linear OA(5107, 15647, F5, 22) (dual of [15647, 15540, 23]-code) | [i] | ✔ | |
| 16 | Linear OA(589, 15647, F5, 18) (dual of [15647, 15558, 19]-code) | [i] | ✔ | |
| 17 | Linear OA(5116, 15651, F5, 23) (dual of [15651, 15535, 24]-code) | [i] | ✔ | |
| 18 | Linear OA(5117, 15657, F5, 23) (dual of [15657, 15540, 24]-code) | [i] | ✔ | |
| 19 | Linear OA(592, 15651, F5, 18) (dual of [15651, 15559, 19]-code) | [i] | ✔ | |
| 20 | Linear OA(593, 15657, F5, 18) (dual of [15657, 15564, 19]-code) | [i] | ✔ | |
| 21 | Linear OA(5125, 15665, F5, 24) (dual of [15665, 15540, 25]-code) | [i] | ✔ | |
| 22 | Linear OA(595, 15665, F5, 18) (dual of [15665, 15570, 19]-code) | [i] | ✔ | |
| 23 | Linear OA(5135, 15675, F5, 26) (dual of [15675, 15540, 27]-code) | [i] | ✔ | |
| 24 | Linear OA(5133, 15673, F5, 25) (dual of [15673, 15540, 26]-code) | [i] | ✔ | |
| 25 | Linear OA(597, 15673, F5, 18) (dual of [15673, 15576, 19]-code) | [i] | ✔ | |
| 26 | Linear OA(5145, 15685, F5, 27) (dual of [15685, 15540, 28]-code) | [i] | ✔ | |
| 27 | Linear OA(5115, 15655, F5, 23) (dual of [15655, 15540, 24]-code) | [i] | ✔ | |
| 28 | Linear OA(591, 15655, F5, 18) (dual of [15655, 15564, 19]-code) | [i] | ✔ | |
| 29 | Linear OA(5123, 15658, F5, 24) (dual of [15658, 15535, 25]-code) | [i] | ✔ | |
| 30 | Linear OA(5124, 15664, F5, 24) (dual of [15664, 15540, 25]-code) | [i] | ✔ | |
| 31 | Linear OA(593, 15658, F5, 18) (dual of [15658, 15565, 19]-code) | [i] | ✔ | |
| 32 | Linear OA(594, 15664, F5, 18) (dual of [15664, 15570, 19]-code) | [i] | ✔ | |
| 33 | Linear OA(5132, 15670, F5, 25) (dual of [15670, 15538, 26]-code) | [i] | ✔ | |
| 34 | Linear OA(596, 15670, F5, 18) (dual of [15670, 15574, 19]-code) | [i] | ✔ | |
| 35 | Linear OA(5134, 15674, F5, 26) (dual of [15674, 15540, 27]-code) | [i] | ✔ | |
| 36 | Linear OA(5124, 15659, F5, 24) (dual of [15659, 15535, 25]-code) | [i] | ✔ | Construction XX with a Chain of Extended Narrow-Sense BCH Codes |
| 37 | Linear OA(5116, 15653, F5, 23) (dual of [15653, 15537, 24]-code) | [i] | ✔ | |
| 38 | Linear OA(5115, 15651, F5, 23) (dual of [15651, 15536, 24]-code) | [i] | ✔ | |
| 39 | Linear OA(5114, 15649, F5, 23) (dual of [15649, 15535, 24]-code) | [i] | ✔ | |
| 40 | Linear OA(5118, 15659, F5, 23) (dual of [15659, 15541, 24]-code) | [i] | ✔ | |
| 41 | Linear OA(5110, 15653, F5, 22) (dual of [15653, 15543, 23]-code) | [i] | ✔ | |
| 42 | Linear OA(5109, 15651, F5, 22) (dual of [15651, 15542, 23]-code) | [i] | ✔ | |
| 43 | Linear OA(5108, 15649, F5, 22) (dual of [15649, 15541, 23]-code) | [i] | ✔ | |
| 44 | Linear OA(599, 15634, F5, 21) (dual of [15634, 15535, 22]-code) | [i] | ✔ | |
| 45 | Linear OA(599, 15640, F5, 20) (dual of [15640, 15541, 21]-code) | [i] | ✔ | |
| 46 | Linear OA(588, 15641, F5, 18) (dual of [15641, 15553, 19]-code) | [i] | ✔ | |
| 47 | Linear OA(592, 15653, F5, 18) (dual of [15653, 15561, 19]-code) | [i] | ✔ | |
| 48 | Linear OA(591, 15651, F5, 18) (dual of [15651, 15560, 19]-code) | [i] | ✔ | |
| 49 | Linear OA(590, 15649, F5, 18) (dual of [15649, 15559, 19]-code) | [i] | ✔ | |
| 50 | Linear OA(594, 15659, F5, 18) (dual of [15659, 15565, 19]-code) | [i] | ✔ | |
| 51 | Linear OOA(585, 1736, F5, 18, 18) (dual of [(1736, 18), 31163, 19]-NRT-code) | [i] | OA Folding and Stacking | |