Information on Result #682647
Linear OA(561, 15625, F5, 13) (dual of [15625, 15564, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13
Mode: Constructive and linear.
This result is hidden, because other results with identical parameters exist.
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 OOA(561, 7964, F5, 2, 13) (dual of [(7964, 2), 15867, 14]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(561, 7964, F5, 3, 13) (dual of [(7964, 3), 23831, 14]-NRT-code) | [i] | ||
| 3 | Digital (48, 61, 7964)-net over F5 | [i] | ||
| 4 | Linear OA(567, 15631, F5, 14) (dual of [15631, 15564, 15]-code) | [i] | ✔ | Construction X with Extended Narrow-Sense BCH Codes |
| 5 | Linear OA(561, 15631, F5, 13) (dual of [15631, 15570, 14]-code) | [i] | ✔ | |
| 6 | Linear OA(576, 15640, F5, 16) (dual of [15640, 15564, 17]-code) | [i] | ✔ | |
| 7 | Linear OA(583, 15647, F5, 17) (dual of [15647, 15564, 18]-code) | [i] | ✔ | |
| 8 | Linear OA(565, 15647, F5, 13) (dual of [15647, 15582, 14]-code) | [i] | ✔ | |
| 9 | Linear OA(592, 15651, F5, 18) (dual of [15651, 15559, 19]-code) | [i] | ✔ | |
| 10 | Linear OA(593, 15657, F5, 18) (dual of [15657, 15564, 19]-code) | [i] | ✔ | |
| 11 | Linear OA(568, 15651, F5, 13) (dual of [15651, 15583, 14]-code) | [i] | ✔ | |
| 12 | Linear OA(569, 15657, F5, 13) (dual of [15657, 15588, 14]-code) | [i] | ✔ | |
| 13 | Linear OA(5101, 15665, F5, 19) (dual of [15665, 15564, 20]-code) | [i] | ✔ | |
| 14 | Linear OA(591, 15655, F5, 18) (dual of [15655, 15564, 19]-code) | [i] | ✔ | |
| 15 | Linear OA(567, 15655, F5, 13) (dual of [15655, 15588, 14]-code) | [i] | ✔ | |
| 16 | Linear OA(599, 15658, F5, 19) (dual of [15658, 15559, 20]-code) | [i] | ✔ | |
| 17 | Linear OA(5100, 15664, F5, 19) (dual of [15664, 15564, 20]-code) | [i] | ✔ | |
| 18 | Linear OA(570, 15664, F5, 13) (dual of [15664, 15594, 14]-code) | [i] | ✔ | |
| 19 | Linear OA(5100, 15659, F5, 19) (dual of [15659, 15559, 20]-code) | [i] | ✔ | Construction XX with a Chain of Extended Narrow-Sense BCH Codes |
| 20 | Linear OA(592, 15653, F5, 18) (dual of [15653, 15561, 19]-code) | [i] | ✔ | |
| 21 | Linear OA(591, 15651, F5, 18) (dual of [15651, 15560, 19]-code) | [i] | ✔ | |
| 22 | Linear OA(590, 15649, F5, 18) (dual of [15649, 15559, 19]-code) | [i] | ✔ | |
| 23 | Linear OA(594, 15659, F5, 18) (dual of [15659, 15565, 19]-code) | [i] | ✔ | |
| 24 | Linear OA(586, 15653, F5, 17) (dual of [15653, 15567, 18]-code) | [i] | ✔ | |
| 25 | Linear OA(585, 15651, F5, 17) (dual of [15651, 15566, 18]-code) | [i] | ✔ | |
| 26 | Linear OA(584, 15649, F5, 17) (dual of [15649, 15565, 18]-code) | [i] | ✔ | |
| 27 | Linear OA(575, 15634, F5, 16) (dual of [15634, 15559, 17]-code) | [i] | ✔ | |
| 28 | Linear OA(568, 15653, F5, 13) (dual of [15653, 15585, 14]-code) | [i] | ✔ | |
| 29 | Linear OA(567, 15651, F5, 13) (dual of [15651, 15584, 14]-code) | [i] | ✔ | |
| 30 | Linear OA(566, 15649, F5, 13) (dual of [15649, 15583, 14]-code) | [i] | ✔ | |
| 31 | Linear OA(570, 15659, F5, 13) (dual of [15659, 15589, 14]-code) | [i] | ✔ | |