Information on Result #682976
Linear OA(551, 3125, F5, 13) (dual of [3125, 3074, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, 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(551, 1838, F5, 2, 13) (dual of [(1838, 2), 3625, 14]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(551, 1838, F5, 3, 13) (dual of [(1838, 3), 5463, 14]-NRT-code) | [i] | ||
| 3 | Digital (38, 51, 1838)-net over F5 | [i] | ||
| 4 | Linear OA(556, 3130, F5, 14) (dual of [3130, 3074, 15]-code) | [i] | ✔ | Construction X with Extended Narrow-Sense BCH Codes |
| 5 | Linear OA(551, 3130, F5, 13) (dual of [3130, 3079, 14]-code) | [i] | ✔ | |
| 6 | Linear OA(564, 3138, F5, 16) (dual of [3138, 3074, 17]-code) | [i] | ✔ | |
| 7 | Linear OA(570, 3144, F5, 17) (dual of [3144, 3074, 18]-code) | [i] | ✔ | |
| 8 | Linear OA(555, 3144, F5, 13) (dual of [3144, 3089, 14]-code) | [i] | ✔ | |
| 9 | Linear OA(578, 3151, F5, 18) (dual of [3151, 3073, 19]-code) | [i] | ✔ | |
| 10 | Linear OA(579, 3153, F5, 18) (dual of [3153, 3074, 19]-code) | [i] | ✔ | |
| 11 | Linear OA(558, 3151, F5, 13) (dual of [3151, 3093, 14]-code) | [i] | ✔ | |
| 12 | Linear OA(559, 3153, F5, 13) (dual of [3153, 3094, 14]-code) | [i] | ✔ | |
| 13 | Linear OA(586, 3160, F5, 19) (dual of [3160, 3074, 20]-code) | [i] | ✔ | |
| 14 | Linear OA(577, 3151, F5, 18) (dual of [3151, 3074, 19]-code) | [i] | ✔ | |
| 15 | Linear OA(557, 3151, F5, 13) (dual of [3151, 3094, 14]-code) | [i] | ✔ | |
| 16 | Linear OA(583, 3153, F5, 19) (dual of [3153, 3070, 20]-code) | [i] | ✔ | |
| 17 | Linear OA(584, 3158, F5, 19) (dual of [3158, 3074, 20]-code) | [i] | ✔ | |
| 18 | Linear OA(559, 3158, F5, 13) (dual of [3158, 3099, 14]-code) | [i] | ✔ | |
| 19 | Linear OA(585, 3155, F5, 19) (dual of [3155, 3070, 20]-code) | [i] | ✔ | Construction XX with a Chain of Extended Narrow-Sense BCH Codes |
| 20 | Linear OA(577, 3148, F5, 18) (dual of [3148, 3071, 19]-code) | [i] | ✔ | |
| 21 | Linear OA(576, 3146, F5, 18) (dual of [3146, 3070, 19]-code) | [i] | ✔ | |
| 22 | Linear OA(580, 3155, F5, 18) (dual of [3155, 3075, 19]-code) | [i] | ✔ | |
| 23 | Linear OA(572, 3148, F5, 17) (dual of [3148, 3076, 18]-code) | [i] | ✔ | |
| 24 | Linear OA(571, 3146, F5, 17) (dual of [3146, 3075, 18]-code) | [i] | ✔ | |
| 25 | Linear OA(563, 3133, F5, 16) (dual of [3133, 3070, 17]-code) | [i] | ✔ | |
| 26 | Linear OA(557, 3148, F5, 13) (dual of [3148, 3091, 14]-code) | [i] | ✔ | |
| 27 | Linear OA(556, 3146, F5, 13) (dual of [3146, 3090, 14]-code) | [i] | ✔ | |