Information on Result #658934
Linear OA(871, 94, F8, 41) (dual of [94, 23, 42]-code), using construction XX applied to AG(F,23P) ⊂ AG(F,34P) ⊂ AG(F,36P) based on
- linear OA(853, 64, F8, 41) (dual of [64, 11, 42]-code), using algebraic-geometric code AG(F,23P) with known gap numbers [i] based on function field F/F8 with g(F) = 14 and N(F) ≥ 65, using the Suzuki function field over F8 [i]
- linear OA(843, 64, F8, 29) (dual of [64, 21, 30]-code), using algebraic-geometric code AG(F,34P) [i] based on function field F/F8 with g(F) = 14 and N(F) ≥ 65 (see above)
- linear OA(841, 64, F8, 27) (dual of [64, 23, 28]-code), using algebraic-geometric code AG(F,36P) [i] based on function field F/F8 with g(F) = 14 and N(F) ≥ 65 (see above)
- linear OA(815, 27, F8, 11) (dual of [27, 12, 12]-code), using
- construction X applied to AG(F,6P) ⊂ AG(F,7P) [i] 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(812, 24, F8, 9) (dual of [24, 12, 10]-code), using algebraic-geometric code AG(F,7P) with degPÂ =Â 2 [i] based on function field F/F8 with g(F) = 3 and N(F) ≥ 24 (see above)
- linear OA(81, 3, F8, 1) (dual of [3, 2, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(81, s, F8, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to AG(F,6P) ⊂ AG(F,7P) [i] based on
- linear OA(81, 3, F8, 1) (dual of [3, 2, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(81, 8, F8, 1) (dual of [8, 7, 2]-code), using
- Reed–Solomon code RS(7,8) [i]
- discarding factors / shortening the dual code based on linear OA(81, 8, F8, 1) (dual of [8, 7, 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:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(871, 47, F8, 2, 41) (dual of [(47, 2), 23, 42]-NRT-code) | [i] | OOA Folding | |