Information on Result #613604
Linear OA(531, 3125, F5, 8) (dual of [3125, 3094, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8
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(535, 3131, F5, 8) (dual of [3131, 3096, 9]-code) | [i] | (u, u+v)-Construction | |
| 2 | Linear OOA(531, 2335, F5, 2, 8) (dual of [(2335, 2), 4639, 9]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(531, 2335, F5, 3, 8) (dual of [(2335, 3), 6974, 9]-NRT-code) | [i] | ||
| 4 | Digital (23, 31, 2335)-net over F5 | [i] | ||
| 5 | Linear OA(536, 3130, F5, 9) (dual of [3130, 3094, 10]-code) | [i] | ✔ | Construction X with Extended Narrow-Sense BCH Codes |
| 6 | Linear OA(531, 3130, F5, 8) (dual of [3130, 3099, 9]-code) | [i] | ✔ | |
| 7 | Linear OA(542, 3136, F5, 10) (dual of [3136, 3094, 11]-code) | [i] | ✔ | |
| 8 | Linear OA(544, 3138, F5, 11) (dual of [3138, 3094, 12]-code) | [i] | ✔ | |
| 9 | Linear OA(532, 3136, F5, 8) (dual of [3136, 3104, 9]-code) | [i] | ✔ | |
| 10 | Linear OA(550, 3144, F5, 12) (dual of [3144, 3094, 13]-code) | [i] | ✔ | |
| 11 | Linear OA(535, 3144, F5, 8) (dual of [3144, 3109, 9]-code) | [i] | ✔ | |
| 12 | Linear OA(558, 3151, F5, 13) (dual of [3151, 3093, 14]-code) | [i] | ✔ | |
| 13 | Linear OA(559, 3153, F5, 13) (dual of [3153, 3094, 14]-code) | [i] | ✔ | |
| 14 | Linear OA(557, 3151, F5, 13) (dual of [3151, 3094, 14]-code) | [i] | ✔ | |
| 15 | Linear OA(563, 3153, F5, 14) (dual of [3153, 3090, 15]-code) | [i] | ✔ | |
| 16 | Linear OA(564, 3158, F5, 14) (dual of [3158, 3094, 15]-code) | [i] | ✔ | |
| 17 | Linear OA(565, 3155, F5, 14) (dual of [3155, 3090, 15]-code) | [i] | ✔ | Construction XX with a Chain of Extended Narrow-Sense BCH Codes |
| 18 | Linear OA(557, 3148, F5, 13) (dual of [3148, 3091, 14]-code) | [i] | ✔ | |
| 19 | Linear OA(556, 3146, F5, 13) (dual of [3146, 3090, 14]-code) | [i] | ✔ | |
| 20 | Linear OA(552, 3148, F5, 12) (dual of [3148, 3096, 13]-code) | [i] | ✔ | |
| 21 | Linear OA(551, 3146, F5, 12) (dual of [3146, 3095, 13]-code) | [i] | ✔ | |
| 22 | Linear OA(543, 3133, F5, 11) (dual of [3133, 3090, 12]-code) | [i] | ✔ | |
| 23 | Linear OA(542, 3137, F5, 10) (dual of [3137, 3095, 11]-code) | [i] | ✔ | Construction X4 with Extended Narrow-Sense BCH Codes |
| 24 | Linear OA(532, 3137, F5, 8) (dual of [3137, 3105, 9]-code) | [i] | ✔ | |