Information on Result #645323
Linear OA(1678, 100, F16, 53) (dual of [100, 22, 54]-code), using construction X applied to AG(F,10P) ⊂ AG(F,27P) based on
- linear OA(1659, 64, F16, 53) (dual of [64, 5, 54]-code), using algebraic-geometric code AG(F,10P) [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(1642, 64, F16, 36) (dual of [64, 22, 37]-code), using algebraic-geometric code AG(F,27P) [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65 (see above)
- linear OA(1619, 36, F16, 16) (dual of [36, 17, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(1619, 38, F16, 16) (dual of [38, 19, 17]-code), using
- extended algebraic-geometric code AGe(F,21P) [i] based on function field F/F16 with g(F) = 3 and N(F) ≥ 38, using
- discarding factors / shortening the dual code based on linear OA(1619, 38, F16, 16) (dual of [38, 19, 17]-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(1678, 50, F16, 2, 53) (dual of [(50, 2), 22, 54]-NRT-code) | [i] | OOA Folding | |