Information on Result #614857
Linear OA(857, 2097152, F8, 10) (dual of [2097152, 2097095, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10
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(862, 2097161, F8, 10) (dual of [2097161, 2097099, 11]-code) | [i] | (u, u+v)-Construction | |
| 2 | Linear OA(863, 2097166, F8, 10) (dual of [2097166, 2097103, 11]-code) | [i] | ||
| 3 | Linear OA(864, 2097209, F8, 10) (dual of [2097209, 2097145, 11]-code) | [i] | ||
| 4 | Linear OOA(857, 1127769, F8, 2, 10) (dual of [(1127769, 2), 2255481, 11]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 5 | Linear OOA(857, 1127769, F8, 3, 10) (dual of [(1127769, 3), 3383250, 11]-NRT-code) | [i] | ||
| 6 | Digital (47, 57, 1127769)-net over F8 | [i] | ||
| 7 | Linear OA(864, 2097160, F8, 10) (dual of [2097160, 2097096, 11]-code) | [i] | (u, u−v, u+v+w)-Construction | |
| 8 | Linear OA(864, 2097159, F8, 11) (dual of [2097159, 2097095, 12]-code) | [i] | ✔ | Construction X with Extended Narrow-Sense BCH Codes |
| 9 | Linear OA(857, 2097159, F8, 10) (dual of [2097159, 2097102, 11]-code) | [i] | ✔ | |
| 10 | Linear OA(872, 2097167, F8, 12) (dual of [2097167, 2097095, 13]-code) | [i] | ✔ | |
| 11 | Linear OA(860, 2097169, F8, 10) (dual of [2097169, 2097109, 11]-code) | [i] | ✔ | |
| 12 | Linear OA(881, 2097176, F8, 13) (dual of [2097176, 2097095, 14]-code) | [i] | ✔ | |
| 13 | Linear OA(861, 2097177, F8, 10) (dual of [2097177, 2097116, 11]-code) | [i] | ✔ | |
| 14 | Linear OA(889, 2097184, F8, 14) (dual of [2097184, 2097095, 15]-code) | [i] | ✔ | |
| 15 | Linear OA(863, 2097186, F8, 10) (dual of [2097186, 2097123, 11]-code) | [i] | ✔ | |
| 16 | Linear OA(898, 2097193, F8, 15) (dual of [2097193, 2097095, 16]-code) | [i] | ✔ | |
| 17 | Linear OA(8110, 2097205, F8, 17) (dual of [2097205, 2097095, 18]-code) | [i] | ✔ | |
| 18 | Linear OA(8106, 2097201, F8, 16) (dual of [2097201, 2097095, 17]-code) | [i] | ✔ | |
| 19 | Linear OA(8119, 2097214, F8, 18) (dual of [2097214, 2097095, 19]-code) | [i] | ✔ | |
| 20 | Linear OA(8109, 2097204, F8, 17) (dual of [2097204, 2097095, 18]-code) | [i] | ✔ | |
| 21 | Linear OA(8118, 2097213, F8, 18) (dual of [2097213, 2097095, 19]-code) | [i] | ✔ | |
| 22 | Linear OA(859, 2097162, F8, 10) (dual of [2097162, 2097103, 11]-code) | [i] | ✔ | Construction XX with a Chain of Extended Narrow-Sense BCH Codes |
| 23 | Linear OA(862, 2097179, F8, 10) (dual of [2097179, 2097117, 11]-code) | [i] | ✔ | |
| 24 | Linear OA(872, 2097168, F8, 12) (dual of [2097168, 2097096, 13]-code) | [i] | ✔ | Construction X4 with Extended Narrow-Sense BCH Codes |