Information on Result #644749
Linear OA(1643, 67, F16, 36) (dual of [67, 24, 37]-code), using construction X applied to AG(F,27P) ⊂ AG(F,29P) based on
- linear OA(1642, 64, F16, 36) (dual of [64, 22, 37]-code), using algebraic-geometric code AG(F,27P) [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(1640, 64, F16, 34) (dual of [64, 24, 35]-code), using algebraic-geometric code AG(F,29P) [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65 (see above)
- linear OA(161, 3, F16, 1) (dual of [3, 2, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(161, s, F16, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, 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(16110, 134, F16, 73) (dual of [134, 24, 74]-code) | [i] | Repeating Each Code Word | |
| 2 | Linear OA(486, 134, F4, 36) (dual of [134, 48, 37]-code) | [i] | Trace Code | |
| 3 | Linear OA(16108, 132, F16, 72) (dual of [132, 24, 73]-code) | [i] | Juxtaposition | |
| 4 | Linear OA(2239, 335, F2, 73) (dual of [335, 96, 74]-code) | [i] | Concatenation of Two Codes | |
| 5 | Linear OOA(1643, 33, F16, 2, 36) (dual of [(33, 2), 23, 37]-NRT-code) | [i] | OOA Folding | |