Information on Result #657089
Linear OA(813, 27, F8, 9) (dual of [27, 14, 10]-code), using construction X applied to AG(F,7P) ⊂ AG(F,8P) based on
- linear OA(812, 24, F8, 9) (dual of [24, 12, 10]-code), using algebraic-geometric code AG(F,7P) 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(810, 24, F8, 7) (dual of [24, 14, 8]-code), using algebraic-geometric code AG(F,8P) 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(894, 32796, F8, 19) (dual of [32796, 32702, 20]-code) | [i] | (u, u+v)-Construction | |
| 2 | Linear OA(8126, 2097180, F8, 19) (dual of [2097180, 2097054, 20]-code) | [i] | ||
| 3 | Linear OA(889, 32795, F8, 18) (dual of [32795, 32706, 19]-code) | [i] | ||
| 4 | Linear OA(8119, 2097179, F8, 18) (dual of [2097179, 2097060, 19]-code) | [i] | ||
| 5 | Linear OA(860, 92, F8, 31) (dual of [92, 32, 32]-code) | [i] | Construction XX with a Chain of Extended Narrow-Sense BCH Codes | |
| 6 | Linear OA(858, 92, F8, 30) (dual of [92, 34, 31]-code) | [i] | ||
| 7 | Linear OA(856, 92, F8, 29) (dual of [92, 36, 30]-code) | [i] | ||