Information on Result #659002
Linear OA(16115, 134, F16, 83) (dual of [134, 19, 84]-code), using repeating each code word 2 times based on linear OA(1648, 67, F16, 41) (dual of [67, 19, 42]-code), using
- construction X applied to AG(F,22P) ⊂ AG(F,24P) [i] based on
- linear OA(1647, 64, F16, 41) (dual of [64, 17, 42]-code), using algebraic-geometric code AG(F,22P) [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(1645, 64, F16, 39) (dual of [64, 19, 40]-code), using algebraic-geometric code AG(F,24P) [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
- linear OA(1647, 64, F16, 41) (dual of [64, 17, 42]-code), using algebraic-geometric code AG(F,22P) [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, 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(16115, 134, F16, 82) (dual of [134, 19, 83]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(16114, 133, F16, 82) (dual of [133, 19, 83]-code) | [i] | Truncation | |
| 3 | Linear OOA(16115, 67, F16, 2, 83) (dual of [(67, 2), 19, 84]-NRT-code) | [i] | OOA Folding | |