Information on Result #644135
Linear OA(819, 30, F8, 13) (dual of [30, 11, 14]-code), using construction X applied to AG(F,9P) ⊂ AG(F,13P) based on
- linear OA(816, 23, F8, 13) (dual of [23, 7, 14]-code), using algebraic-geometric code AG(F,9P) [i] based on function field F/F8 with g(F) = 3 and N(F) ≥ 24, using
- the Klein quartic over F8 [i]
- linear OA(812, 23, F8, 9) (dual of [23, 11, 10]-code), using algebraic-geometric code AG(F,13P) [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(877, 94, F8, 47) (dual of [94, 17, 48]-code) | [i] | Construction X with Algebraic-Geometric Codes | |
| 2 | Linear OA(879, 94, F8, 51) (dual of [94, 15, 52]-code) | [i] | Construction X with Extended Narrow-Sense BCH Codes | |
| 3 | Linear OA(874, 94, F8, 44) (dual of [94, 20, 45]-code) | [i] | ||
| 4 | Linear OOA(819, 15, F8, 2, 13) (dual of [(15, 2), 11, 14]-NRT-code) | [i] | OOA Folding | |