Information on Result #657083

Linear OA(819, 27, F8, 15) (dual of [27, 8, 16]-code), using construction X applied to AG(F,4P) ⊂ AG(F,5P) based on
  1. linear OA(818, 24, F8, 15) (dual of [24, 6, 16]-code), using algebraic-geometric code AG(F,4P) with degP = 2 [i] based on function field F/F8 with g(F) = 3 and N(F) ≥ 24, using the Klein quartic over F8 [i]
  2. linear OA(816, 24, F8, 13) (dual of [24, 8, 14]-code), using algebraic-geometric code AG(F,5P) with degP = 2 [i] based on function field F/F8 with g(F) = 3 and N(F) ≥ 24 (see above)
  3. linear OA(81, 3, F8, 1) (dual of [3, 2, 2]-code), 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:

ResultThis
result
only		Method
1Linear OA(8101, 539, F8, 31) (dual of [539, 438, 32]-code) [i](u, u+v)-Construction
2Linear OA(8155, 32795, F8, 31) (dual of [32795, 32640, 32]-code) [i]
3Linear OA(8150, 32795, F8, 30) (dual of [32795, 32645, 31]-code) [i]
4Linear OA(883, 91, F8, 62) (dual of [91, 8, 63]-code) [i]Juxtaposition
5Linear OA(895, 103, F8, 70) (dual of [103, 8, 71]-code) [i]
6Linear OOA(2138, 81, F2, 2, 63) (dual of [(81, 2), 24, 64]-NRT-code) [i]Concatenation of Two NRT-Codes
7Linear OOA(2138, 54, F2, 3, 63) (dual of [(54, 3), 24, 64]-NRT-code) [i]
8Linear OOA(2219, 81, F2, 3, 111) (dual of [(81, 3), 24, 112]-NRT-code) [i]
9Linear OA(889, 100, F8, 61) (dual of [100, 11, 62]-code) [i]Construction X with Cyclic Codes
10Linear OA(882, 91, F8, 61) (dual of [91, 9, 62]-code) [i]Construction X with Extended Narrow-Sense BCH Codes
11Linear OA(883, 92, F8, 62) (dual of [92, 9, 63]-code) [i]Construction XX with a Chain of Extended Narrow-Sense BCH Codes