Information on Result #658952
Linear OA(824, 29, F8, 19) (dual of [29, 5, 20]-code), using construction X applied to AG(F,3P) ⊂ AG(F,7P) based on
- linear OA(821, 23, F8, 19) (dual of [23, 2, 20]-code), using algebraic-geometric code AG(F,3P) with known gap numbers [i] based on function field F/F8 with g(F) = 3 and N(F) ≥ 24, using the Klein quartic over F8 [i]
- linear OA(818, 23, F8, 15) (dual of [23, 5, 16]-code), using algebraic-geometric code AG(F,7P) [i] based on function field F/F8 with g(F) = 3 and N(F) ≥ 24 (see above)
- linear OA(83, 6, F8, 3) (dual of [6, 3, 4]-code or 6-arc in PG(2,8) or 6-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(8127, 542, F8, 39) (dual of [542, 415, 40]-code) | [i] | (u, u+v)-Construction | |
| 2 | Linear OA(894, 99, F8, 75) (dual of [99, 5, 76]-code) | [i] | Juxtaposition | |