Information on Result #658680
Linear OA(1682, 101, F16, 58) (dual of [101, 19, 59]-code), using construction X applied to AG(F,5P) ⊂ AG(F,24P) based on
- linear OA(1661, 64, F16, 58) (dual of [64, 3, 59]-code), using algebraic-geometric code AG(F,5P) with known gap numbers [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(1645, 64, F16, 39) (dual of [64, 19, 40]-code), using algebraic-geometric code AG(F,24P) [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65 (see above)
- linear OA(1621, 37, F16, 18) (dual of [37, 16, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(1621, 38, F16, 18) (dual of [38, 17, 19]-code), using
- extended algebraic-geometric code AGe(F,19P) [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(1621, 38, F16, 18) (dual of [38, 17, 19]-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(1683, 102, F16, 58) (dual of [102, 19, 59]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(1681, 100, F16, 57) (dual of [100, 19, 58]-code) | [i] | Truncation | |
| 3 | Linear OA(1680, 99, F16, 56) (dual of [99, 19, 57]-code) | [i] | ||
| 4 | Linear OOA(1682, 50, F16, 2, 58) (dual of [(50, 2), 18, 59]-NRT-code) | [i] | OOA Folding | |