Information on Result #664819
Linear OA(16101, 587, F16, 37) (dual of [587, 486, 38]-code), using (u, u+v)-construction based on
- linear OA(1625, 67, F16, 18) (dual of [67, 42, 19]-code), using
- construction X applied to AG(F,45P) ⊂ AG(F,47P) [i] based on
- linear OA(1624, 64, F16, 18) (dual of [64, 40, 19]-code), using algebraic-geometric code AG(F,45P) [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- the Hermitian function field over F16 [i]
- linear OA(1622, 64, F16, 16) (dual of [64, 42, 17]-code), using algebraic-geometric code AG(F,47P) [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65 (see above)
- linear OA(161, 3, F16, 1) (dual of [3, 2, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(161, s, F16, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- linear OA(1624, 64, F16, 18) (dual of [64, 40, 19]-code), using algebraic-geometric code AG(F,45P) [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- construction X applied to AG(F,45P) ⊂ AG(F,47P) [i] based on
- linear OA(1676, 520, F16, 37) (dual of [520, 444, 38]-code), using
- trace code [i] based on linear OA(25638, 260, F256, 37) (dual of [260, 222, 38]-code), using
- construction X applied to AG(F, Q+108P) ⊂ AG(F, Q+109P) [i] based on
- linear OA(25637, 257, F256, 37) (dual of [257, 220, 38]-code or 257-arc in PG(36,256)), using algebraic-geometric code AG(F, Q+108P) with degQ = 3 and degPÂ =Â 2 [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257, using the rational function field F256(x) [i]
- linear OA(25635, 257, F256, 35) (dual of [257, 222, 36]-code or 257-arc in PG(34,256)), using algebraic-geometric code AG(F, Q+109P) with degQ = 3 and degPÂ =Â 2 [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257 (see above)
- linear OA(2561, 3, F256, 1) (dual of [3, 2, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(2561, s, F256, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to AG(F, Q+108P) ⊂ AG(F, Q+109P) [i] based on
- trace code [i] based on linear OA(25638, 260, F256, 37) (dual of [260, 222, 38]-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.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(16101, 293, F16, 2, 37) (dual of [(293, 2), 485, 38]-NRT-code) | [i] | OOA Folding | |