Information on Result #645019
Linear OA(1677, 86, F16, 63) (dual of [86, 9, 64]-code), using construction X applied to AG(F,0P) ⊂ AG(F,14P) based on
- linear OA(1663, 64, F16, 63) (dual of [64, 1, 64]-code or 64-arc in PG(62,16)), using algebraic-geometric code AG(F,0P) [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(1655, 64, F16, 49) (dual of [64, 9, 50]-code), using algebraic-geometric code AG(F,14P) [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65 (see above)
- linear OA(1614, 22, F16, 13) (dual of [22, 8, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(1614, 24, F16, 13) (dual of [24, 10, 14]-code), using
- extended algebraic-geometric code AGe(F,10P) [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 OA(1614, 24, F16, 13) (dual of [24, 10, 14]-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 OA(1675, 84, F16, 61) (dual of [84, 9, 62]-code) | [i] | Truncation | |
| 2 | Linear OA(1674, 83, F16, 60) (dual of [83, 9, 61]-code) | [i] | ||
| 3 | Linear OOA(1677, 43, F16, 2, 63) (dual of [(43, 2), 9, 64]-NRT-code) | [i] | OOA Folding | |