Information on Result #619599
Linear OA(12846, 2097152, F128, 16) (dual of [2097152, 2097106, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16
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(12854, 2097281, F128, 16) (dual of [2097281, 2097227, 17]-code) | [i] | (u, u+v)-Construction | |
| 2 | Linear OA(12855, 2097302, F128, 16) (dual of [2097302, 2097247, 17]-code) | [i] | ||
| 3 | Linear OA(12856, 2097304, F128, 16) (dual of [2097304, 2097248, 17]-code) | [i] | ||
| 4 | Linear OA(12857, 2097344, F128, 16) (dual of [2097344, 2097287, 17]-code) | [i] | ||
| 5 | Linear OA(12858, 2097408, F128, 16) (dual of [2097408, 2097350, 17]-code) | [i] | ||
| 6 | Linear OA(12859, 2097534, F128, 16) (dual of [2097534, 2097475, 17]-code) | [i] | ||
| 7 | Linear OA(12860, 2097539, F128, 16) (dual of [2097539, 2097479, 17]-code) | [i] | ||
| 8 | Linear OA(12858, 2097410, F128, 16) (dual of [2097410, 2097352, 17]-code) | [i] | ||
| 9 | Linear OA(12860, 2097167, F128, 16) (dual of [2097167, 2097107, 17]-code) | [i] | Generalized (u, u+v)-Construction | |
| 10 | Linear OA(12857, 2097164, F128, 16) (dual of [2097164, 2097107, 17]-code) | [i] | (u, u−v, u+v+w)-Construction | |
| 11 | Linear OA(12858, 2097166, F128, 16) (dual of [2097166, 2097108, 17]-code) | [i] | ||
| 12 | Linear OA(12859, 2097410, F128, 16) (dual of [2097410, 2097351, 17]-code) | [i] | ||
| 13 | Linear OA(12860, 2097431, F128, 16) (dual of [2097431, 2097371, 17]-code) | [i] | ||
| 14 | Linear OA(12849, 2097155, F128, 17) (dual of [2097155, 2097106, 18]-code) | [i] | ✔ | Construction X with Extended Narrow-Sense BCH Codes |
| 15 | Linear OA(12846, 2097155, F128, 16) (dual of [2097155, 2097109, 17]-code) | [i] | ✔ | |
| 16 | Linear OA(12853, 2097159, F128, 18) (dual of [2097159, 2097106, 19]-code) | [i] | ✔ | |
| 17 | Linear OA(12847, 2097159, F128, 16) (dual of [2097159, 2097112, 17]-code) | [i] | ✔ | |
| 18 | Linear OA(12857, 2097163, F128, 19) (dual of [2097163, 2097106, 20]-code) | [i] | ✔ | |
| 19 | Linear OA(12848, 2097163, F128, 16) (dual of [2097163, 2097115, 17]-code) | [i] | ✔ | |
| 20 | Linear OA(12861, 2097167, F128, 20) (dual of [2097167, 2097106, 21]-code) | [i] | ✔ | |
| 21 | Linear OA(12849, 2097167, F128, 16) (dual of [2097167, 2097118, 17]-code) | [i] | ✔ | |
| 22 | Linear OA(12865, 2097171, F128, 21) (dual of [2097171, 2097106, 22]-code) | [i] | ✔ | |
| 23 | Linear OA(12850, 2097171, F128, 16) (dual of [2097171, 2097121, 17]-code) | [i] | ✔ | |
| 24 | Linear OA(12869, 2097175, F128, 22) (dual of [2097175, 2097106, 23]-code) | [i] | ✔ | |
| 25 | Linear OA(12851, 2097175, F128, 16) (dual of [2097175, 2097124, 17]-code) | [i] | ✔ | |
| 26 | Linear OA(12873, 2097179, F128, 23) (dual of [2097179, 2097106, 24]-code) | [i] | ✔ | |
| 27 | Linear OA(12852, 2097179, F128, 16) (dual of [2097179, 2097127, 17]-code) | [i] | ✔ | |
| 28 | Linear OA(12877, 2097183, F128, 24) (dual of [2097183, 2097106, 25]-code) | [i] | ✔ | |
| 29 | Linear OA(12853, 2097183, F128, 16) (dual of [2097183, 2097130, 17]-code) | [i] | ✔ | |
| 30 | Linear OOA(12846, 524288, F128, 4, 16) (dual of [(524288, 4), 2097106, 17]-NRT-code) | [i] | OOA Folding | |
| 31 | Linear OOA(12846, 262144, F128, 16, 16) (dual of [(262144, 16), 4194258, 17]-NRT-code) | [i] | OA Folding and Stacking | |