Information on Result #664907
Linear OA(1686, 587, F16, 31) (dual of [587, 501, 32]-code), using (u, u+v)-construction based on
- linear OA(1622, 67, F16, 15) (dual of [67, 45, 16]-code), using
- construction X applied to AG(F,48P) ⊂ AG(F,50P) [i] based on
- linear OA(1621, 64, F16, 15) (dual of [64, 43, 16]-code), using algebraic-geometric code AG(F,48P) [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(1619, 64, F16, 13) (dual of [64, 45, 14]-code), using algebraic-geometric code AG(F,50P) [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(1621, 64, F16, 15) (dual of [64, 43, 16]-code), using algebraic-geometric code AG(F,48P) [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- construction X applied to AG(F,48P) ⊂ AG(F,50P) [i] based on
- linear OA(1664, 520, F16, 31) (dual of [520, 456, 32]-code), using
- trace code [i] based on linear OA(25632, 260, F256, 31) (dual of [260, 228, 32]-code), using
- construction X applied to AG(F, Q+111P) ⊂ AG(F, Q+112P) [i] based on
- linear OA(25631, 257, F256, 31) (dual of [257, 226, 32]-code or 257-arc in PG(30,256)), using algebraic-geometric code AG(F, Q+111P) 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(25629, 257, F256, 29) (dual of [257, 228, 30]-code or 257-arc in PG(28,256)), using algebraic-geometric code AG(F, Q+112P) 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+111P) ⊂ AG(F, Q+112P) [i] based on
- trace code [i] based on linear OA(25632, 260, F256, 31) (dual of [260, 228, 32]-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(1686, 293, F16, 2, 31) (dual of [(293, 2), 500, 32]-NRT-code) | [i] | OOA Folding | |