Information on Result #657097

Linear OA(821, 31, F8, 15) (dual of [31, 10, 16]-code), using construction X applied to AG(F,4P) ⊂ AG(F,6P) 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(814, 24, F8, 11) (dual of [24, 10, 12]-code), using algebraic-geometric code AG(F,6P) with degP = 2 [i] based on function field F/F8 with g(F) = 3 and N(F) ≥ 24 (see above)
  3. 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

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(8157, 32799, F8, 31) (dual of [32799, 32642, 32]-code) [i](u, u+v)-Construction
2Linear OA(8152, 32799, F8, 30) (dual of [32799, 32647, 31]-code) [i]
3Linear OOA(2156, 93, F2, 2, 63) (dual of [(93, 2), 30, 64]-NRT-code) [i]Concatenation of Two NRT-Codes
4Linear OOA(2249, 93, F2, 3, 111) (dual of [(93, 3), 30, 112]-NRT-code) [i]
5Linear OA(884, 95, F8, 57) (dual of [95, 11, 58]-code) [i]Construction X with Algebraic-Geometric Codes
6Linear OA(882, 95, F8, 54) (dual of [95, 13, 55]-code) [i]
7Linear OA(880, 94, F8, 53) (dual of [94, 14, 54]-code) [i]Construction X with Cyclic Codes
8Linear OA(882, 96, F8, 54) (dual of [96, 14, 55]-code) [i]Construction XX with a Chain of Extended Narrow-Sense BCH Codes