Information on Result #659076
Linear OA(456, 134, F4, 21) (dual of [134, 78, 22]-code), using trace code based on linear OA(1628, 67, F16, 21) (dual of [67, 39, 22]-code), using
- construction X applied to AG(F,42P) ⊂ AG(F,44P) [i] based on
- linear OA(1627, 64, F16, 21) (dual of [64, 37, 22]-code), using algebraic-geometric code AG(F,42P) [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(1625, 64, F16, 19) (dual of [64, 39, 20]-code), using algebraic-geometric code AG(F,44P) [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(1627, 64, F16, 21) (dual of [64, 37, 22]-code), using algebraic-geometric code AG(F,42P) [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, 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 OA(457, 135, F4, 21) (dual of [135, 78, 22]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(456, 67, F4, 2, 21) (dual of [(67, 2), 78, 22]-NRT-code) | [i] | OOA Folding | |