Information on Result #658648
Linear OA(1674, 87, F16, 58) (dual of [87, 13, 59]-code), using construction X applied to AG(F,5P) ⊂ AG(F,18P) 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(1651, 64, F16, 45) (dual of [64, 13, 46]-code), using algebraic-geometric code AG(F,18P) [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65 (see above)
- linear OA(1613, 23, F16, 12) (dual of [23, 10, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(1613, 24, F16, 12) (dual of [24, 11, 13]-code), using
- extended algebraic-geometric code AGe(F,11P) [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(1613, 24, F16, 12) (dual of [24, 11, 13]-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(1673, 86, F16, 57) (dual of [86, 13, 58]-code) | [i] | Truncation | |
| 2 | Linear OA(1672, 85, F16, 56) (dual of [85, 13, 57]-code) | [i] | ||
| 3 | Linear OOA(1674, 43, F16, 2, 58) (dual of [(43, 2), 12, 59]-NRT-code) | [i] | OOA Folding | |