Information on Result #613771
Linear OA(591, 15625, F5, 19) (dual of [15625, 15534, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19
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(5100, 15635, F5, 19) (dual of [15635, 15535, 20]-code) | [i] | (u, u+v)-Construction | |
| 2 | Linear OA(5101, 15637, F5, 19) (dual of [15637, 15536, 20]-code) | [i] | ||
| 3 | Linear OA(5102, 15639, F5, 19) (dual of [15639, 15537, 20]-code) | [i] | ||
| 4 | Linear OA(5103, 15641, F5, 19) (dual of [15641, 15538, 20]-code) | [i] | ||
| 5 | Linear OA(5104, 15653, F5, 19) (dual of [15653, 15549, 20]-code) | [i] | ||
| 6 | Linear OA(5105, 15640, F5, 19) (dual of [15640, 15535, 20]-code) | [i] | Generalized (u, u+v)-Construction | |
| 7 | Linear OOA(591, 8990, F5, 2, 19) (dual of [(8990, 2), 17889, 20]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 8 | Linear OOA(591, 8990, F5, 3, 19) (dual of [(8990, 3), 26879, 20]-NRT-code) | [i] | ||
| 9 | Digital (72, 91, 8990)-net over F5 | [i] | ||
| 10 | Linear OA(5104, 15639, F5, 19) (dual of [15639, 15535, 20]-code) | [i] | (u, u−v, u+v+w)-Construction | |
| 11 | Linear OA(598, 15632, F5, 21) (dual of [15632, 15534, 22]-code) | [i] | ✔ | Construction X with Extended Narrow-Sense BCH Codes |
| 12 | Linear OA(591, 15631, F5, 19) (dual of [15631, 15540, 20]-code) | [i] | ✔ | |
| 13 | Linear OA(5106, 15640, F5, 22) (dual of [15640, 15534, 23]-code) | [i] | ✔ | |
| 14 | Linear OA(592, 15638, F5, 19) (dual of [15638, 15546, 20]-code) | [i] | ✔ | |
| 15 | Linear OA(5113, 15647, F5, 23) (dual of [15647, 15534, 24]-code) | [i] | ✔ | |
| 16 | Linear OA(594, 15646, F5, 19) (dual of [15646, 15552, 20]-code) | [i] | ✔ | |
| 17 | Linear OA(5122, 15651, F5, 24) (dual of [15651, 15529, 25]-code) | [i] | ✔ | |
| 18 | Linear OA(5123, 15657, F5, 24) (dual of [15657, 15534, 25]-code) | [i] | ✔ | |
| 19 | Linear OA(598, 15651, F5, 19) (dual of [15651, 15553, 20]-code) | [i] | ✔ | |
| 20 | Linear OA(599, 15657, F5, 19) (dual of [15657, 15558, 20]-code) | [i] | ✔ | |
| 21 | Linear OA(5133, 15667, F5, 26) (dual of [15667, 15534, 27]-code) | [i] | ✔ | |
| 22 | Linear OA(5131, 15665, F5, 25) (dual of [15665, 15534, 26]-code) | [i] | ✔ | |
| 23 | Linear OA(5101, 15665, F5, 19) (dual of [15665, 15564, 20]-code) | [i] | ✔ | |
| 24 | Linear OA(5141, 15675, F5, 27) (dual of [15675, 15534, 28]-code) | [i] | ✔ | |
| 25 | Linear OA(5103, 15673, F5, 19) (dual of [15673, 15570, 20]-code) | [i] | ✔ | |
| 26 | Linear OA(5105, 15677, F5, 19) (dual of [15677, 15572, 20]-code) | [i] | ✔ | |
| 27 | Linear OA(5121, 15655, F5, 24) (dual of [15655, 15534, 25]-code) | [i] | ✔ | |
| 28 | Linear OA(597, 15655, F5, 19) (dual of [15655, 15558, 20]-code) | [i] | ✔ | |
| 29 | Linear OA(5132, 15666, F5, 26) (dual of [15666, 15534, 27]-code) | [i] | ✔ | |
| 30 | Linear OA(5130, 15664, F5, 25) (dual of [15664, 15534, 26]-code) | [i] | ✔ | |
| 31 | Linear OA(599, 15658, F5, 19) (dual of [15658, 15559, 20]-code) | [i] | ✔ | |
| 32 | Linear OA(5100, 15664, F5, 19) (dual of [15664, 15564, 20]-code) | [i] | ✔ | |
| 33 | Linear OA(5102, 15670, F5, 19) (dual of [15670, 15568, 20]-code) | [i] | ✔ | |
| 34 | Linear OA(5140, 15674, F5, 27) (dual of [15674, 15534, 28]-code) | [i] | ✔ | |
| 35 | Linear OA(5129, 15659, F5, 25) (dual of [15659, 15530, 26]-code) | [i] | ✔ | Construction XX with a Chain of Extended Narrow-Sense BCH Codes |
| 36 | Linear OA(5131, 15660, F5, 26) (dual of [15660, 15529, 27]-code) | [i] | ✔ | |
| 37 | Linear OA(5122, 15653, F5, 24) (dual of [15653, 15531, 25]-code) | [i] | ✔ | |
| 38 | Linear OA(5121, 15651, F5, 24) (dual of [15651, 15530, 25]-code) | [i] | ✔ | |
| 39 | Linear OA(5120, 15649, F5, 24) (dual of [15649, 15529, 25]-code) | [i] | ✔ | |
| 40 | Linear OA(5124, 15659, F5, 24) (dual of [15659, 15535, 25]-code) | [i] | ✔ | |
| 41 | Linear OA(5116, 15653, F5, 23) (dual of [15653, 15537, 24]-code) | [i] | ✔ | |
| 42 | Linear OA(5115, 15651, F5, 23) (dual of [15651, 15536, 24]-code) | [i] | ✔ | |
| 43 | Linear OA(5114, 15649, F5, 23) (dual of [15649, 15535, 24]-code) | [i] | ✔ | |
| 44 | Linear OA(5105, 15634, F5, 22) (dual of [15634, 15529, 23]-code) | [i] | ✔ | |
| 45 | Linear OA(599, 15634, F5, 21) (dual of [15634, 15535, 22]-code) | [i] | ✔ | |
| 46 | Linear OA(593, 15640, F5, 19) (dual of [15640, 15547, 20]-code) | [i] | ✔ | |
| 47 | Linear OA(598, 15653, F5, 19) (dual of [15653, 15555, 20]-code) | [i] | ✔ | |
| 48 | Linear OA(597, 15651, F5, 19) (dual of [15651, 15554, 20]-code) | [i] | ✔ | |
| 49 | Linear OA(596, 15649, F5, 19) (dual of [15649, 15553, 20]-code) | [i] | ✔ | |
| 50 | Linear OA(5100, 15659, F5, 19) (dual of [15659, 15559, 20]-code) | [i] | ✔ | |
| 51 | Linear OA(5130, 15659, F5, 26) (dual of [15659, 15529, 27]-code) | [i] | ✔ | |
| 52 | Linear OA(592, 15645, F5, 18) (dual of [15645, 15553, 19]-code) | [i] | ✔ | Construction X4 with Extended Narrow-Sense BCH Codes |
| 53 | Linear OOA(591, 1736, F5, 19, 19) (dual of [(1736, 19), 32893, 20]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |