Information on Result #657099
Linear OA(817, 31, F8, 11) (dual of [31, 14, 12]-code), using construction X applied to AG(F,6P) ⊂ AG(F,8P) based on
- 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, 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(83, 7, F8, 3) (dual of [7, 4, 4]-code or 7-arc in PG(2,8) or 7-cap in PG(2,8)), using
- discarding factors / shortening the dual code based on linear OA(83, 8, F8, 3) (dual of [8, 5, 4]-code or 8-arc in PG(2,8) or 8-cap in PG(2,8)), using
- Reed–Solomon code RS(5,8) [i]
- discarding factors / shortening the dual code based on linear OA(83, 8, F8, 3) (dual of [8, 5, 4]-code or 8-arc in PG(2,8) or 8-cap in PG(2,8)), 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(8118, 32800, F8, 23) (dual of [32800, 32682, 24]-code) | [i] | (u, u+v)-Construction | |
| 2 | Linear OA(8158, 2097184, F8, 23) (dual of [2097184, 2097026, 24]-code) | [i] | ||
| 3 | Linear OA(8113, 32799, F8, 22) (dual of [32799, 32686, 23]-code) | [i] | ||
| 4 | Linear OA(8151, 2097183, F8, 22) (dual of [2097183, 2097032, 23]-code) | [i] | ||