Information on Result #644829
Linear OA(1638, 69, F16, 30) (dual of [69, 31, 31]-code), using construction X applied to AG(F,33P) ⊂ AG(F,36P) based on
- linear OA(1636, 64, F16, 30) (dual of [64, 28, 31]-code), using algebraic-geometric code AG(F,33P) [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(1633, 64, F16, 27) (dual of [64, 31, 28]-code), using algebraic-geometric code AG(F,36P) [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65 (see above)
- linear OA(162, 5, F16, 2) (dual of [5, 3, 3]-code or 5-arc in PG(1,16)), using
- discarding factors / shortening the dual code based on linear OA(162, 16, F16, 2) (dual of [16, 14, 3]-code or 16-arc in PG(1,16)), using
- Reed–Solomon code RS(14,16) [i]
- discarding factors / shortening the dual code based on linear OA(162, 16, F16, 2) (dual of [16, 14, 3]-code or 16-arc in PG(1,16)), 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(476, 138, F4, 30) (dual of [138, 62, 31]-code) | [i] | Trace Code | |
| 2 | Linear OA(2221, 345, F2, 61) (dual of [345, 124, 62]-code) | [i] | Concatenation of Two Codes | |
| 3 | Linear OOA(1638, 34, F16, 2, 30) (dual of [(34, 2), 30, 31]-NRT-code) | [i] | OOA Folding | |