Information on Result #930281
Linear OOA(1686, 84, F16, 2, 60) (dual of [(84, 2), 82, 61]-NRT-code), using construction X applied to AG(2;F,67P) ⊂ AG(2;F,87P) based on
- linear OOA(1666, 64, F16, 2, 60) (dual of [(64, 2), 62, 61]-NRT-code), using algebraic-geometric NRT-code AG(2;F,67P) [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- the Hermitian function field over F16 [i]
- linear OOA(1646, 64, F16, 2, 40) (dual of [(64, 2), 82, 41]-NRT-code), using algebraic-geometric NRT-code AG(2;F,87P) [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65 (see above)
- linear OOA(1620, 20, F16, 2, 19) (dual of [(20, 2), 20, 20]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(1620, 24, F16, 2, 19) (dual of [(24, 2), 28, 20]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(2;F,28P) [i] based on function field F/F16 with g(F) = 1 and N(F) ≥ 24, using
- discarding factors / shortening the dual code based on linear OOA(1620, 24, F16, 2, 19) (dual of [(24, 2), 28, 20]-NRT-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(4172, 168, F4, 2, 60) (dual of [(168, 2), 164, 61]-NRT-code) | [i] | Trace Code for OOAs | |