Information on Result #658615
Linear OA(1667, 73, F16, 59) (dual of [73, 6, 60]-code), using construction X applied to AG(F,4P) ⊂ AG(F,10P) based on
- linear OA(1662, 64, F16, 59) (dual of [64, 2, 60]-code), using algebraic-geometric code AG(F,4P) 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(1658, 64, F16, 53) (dual of [64, 6, 54]-code), using algebraic-geometric code AG(F,10P) with known gap numbers [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65 (see above)
- linear OA(165, 9, F16, 5) (dual of [9, 4, 6]-code or 9-arc in PG(4,16)), using
- discarding factors / shortening the dual code based on linear OA(165, 16, F16, 5) (dual of [16, 11, 6]-code or 16-arc in PG(4,16)), using
- Reed–Solomon code RS(11,16) [i]
- discarding factors / shortening the dual code based on linear OA(165, 16, F16, 5) (dual of [16, 11, 6]-code or 16-arc in PG(4,16)), 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(1666, 72, F16, 58) (dual of [72, 6, 59]-code) | [i] | Truncation | |
| 2 | Linear OA(1664, 70, F16, 56) (dual of [70, 6, 57]-code) | [i] | ||
| 3 | Linear OA(16130, 136, F16, 112) (dual of [136, 6, 113]-code) | [i] | Juxtaposition | |
| 4 | Linear OOA(1667, 36, F16, 2, 59) (dual of [(36, 2), 5, 60]-NRT-code) | [i] | OOA Folding | |