Information on Result #658604
Linear OA(1664, 69, F16, 58) (dual of [69, 5, 59]-code), using construction X applied to AG(F,5P) ⊂ AG(F,9P) 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(1659, 64, F16, 54) (dual of [64, 5, 55]-code), using algebraic-geometric code AG(F,9P) with known gap numbers [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65 (see above)
- linear OA(163, 5, F16, 3) (dual of [5, 2, 4]-code or 5-arc in PG(2,16) or 5-cap in PG(2,16)), using
- discarding factors / shortening the dual code based on linear OA(163, 16, F16, 3) (dual of [16, 13, 4]-code or 16-arc in PG(2,16) or 16-cap in PG(2,16)), using
- Reed–Solomon code RS(13,16) [i]
- discarding factors / shortening the dual code based on linear OA(163, 16, F16, 3) (dual of [16, 13, 4]-code or 16-arc in PG(2,16) or 16-cap in PG(2,16)), 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(1663, 68, F16, 57) (dual of [68, 5, 58]-code) | [i] | Truncation | |
| 2 | Linear OA(1662, 67, F16, 56) (dual of [67, 5, 57]-code) | [i] | ||
| 3 | Linear OA(16127, 132, F16, 112) (dual of [132, 5, 113]-code) | [i] | Juxtaposition | |
| 4 | Linear OA(16128, 133, F16, 113) (dual of [133, 5, 114]-code) | [i] | ||
| 5 | Linear OA(16129, 134, F16, 114) (dual of [134, 5, 115]-code) | [i] | ||
| 6 | Linear OOA(1664, 34, F16, 2, 58) (dual of [(34, 2), 4, 59]-NRT-code) | [i] | OOA Folding | |