Information on Result #657085
Linear OA(817, 27, F8, 13) (dual of [27, 10, 14]-code), using construction X applied to AG(F,5P) ⊂ AG(F,6P) based on
- linear OA(816, 24, F8, 13) (dual of [24, 8, 14]-code), using algebraic-geometric code AG(F,5P) with degPÂ =Â 2 [i] based on function field F/F8 with g(F) = 3 and N(F) ≥ 24, using the Klein quartic over F8 [i]
- linear OA(814, 24, F8, 11) (dual of [24, 10, 12]-code), using algebraic-geometric code AG(F,6P) with degPÂ =Â 2 [i] based on function field F/F8 with g(F) = 3 and N(F) ≥ 24 (see above)
- linear OA(81, 3, F8, 1) (dual of [3, 2, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(81, s, F8, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
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.
Compare with Markus Grassl’s online database of code parameters.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OA(887, 539, F8, 27) (dual of [539, 452, 28]-code) | [i] | (u, u+v)-Construction | |
| 2 | Linear OA(8133, 32795, F8, 27) (dual of [32795, 32662, 28]-code) | [i] | ||
| 3 | Linear OA(8156, 262171, F8, 27) (dual of [262171, 262015, 28]-code) | [i] | ||
| 4 | Linear OA(8128, 32795, F8, 26) (dual of [32795, 32667, 27]-code) | [i] | ||
| 5 | Linear OA(8150, 262171, F8, 26) (dual of [262171, 262021, 27]-code) | [i] | ||
| 6 | Linear OA(8172, 2097179, F8, 26) (dual of [2097179, 2097007, 27]-code) | [i] | ||
| 7 | Linear OOA(2132, 81, F2, 2, 55) (dual of [(81, 2), 30, 56]-NRT-code) | [i] | Concatenation of Two NRT-Codes | |
| 8 | Linear OOA(2213, 81, F2, 3, 97) (dual of [(81, 3), 30, 98]-NRT-code) | [i] | ||
| 9 | Linear OA(878, 91, F8, 52) (dual of [91, 13, 53]-code) | [i] | Construction X with Algebraic-Geometric Codes | |
| 10 | Linear OA(877, 91, F8, 51) (dual of [91, 14, 52]-code) | [i] | ||
| 11 | Linear OA(876, 91, F8, 49) (dual of [91, 15, 50]-code) | [i] | ||
| 12 | Linear OA(882, 93, F8, 56) (dual of [93, 11, 57]-code) | [i] | Construction XX with a Chain of Algebraic-Geometric Codes | |
| 13 | Linear OA(882, 95, F8, 55) (dual of [95, 13, 56]-code) | [i] | ||
| 14 | Linear OA(871, 90, F8, 44) (dual of [90, 19, 45]-code) | [i] | Construction X with Cyclic Codes | |
| 15 | Linear OA(876, 90, F8, 51) (dual of [90, 14, 52]-code) | [i] | ||
| 16 | Linear OA(881, 95, F8, 53) (dual of [95, 14, 54]-code) | [i] | Construction XX with a Chain of Cyclic Codes | |
| 17 | Linear OA(872, 91, F8, 44) (dual of [91, 19, 45]-code) | [i] | Construction X with Extended Narrow-Sense BCH Codes | |
| 18 | Linear OA(878, 92, F8, 52) (dual of [92, 14, 53]-code) | [i] | Construction XX with a Chain of Extended Narrow-Sense BCH Codes | |
| 19 | Linear OA(873, 92, F8, 45) (dual of [92, 19, 46]-code) | [i] | ||