Information on Result #658605
Linear OA(1661, 67, F16, 55) (dual of [67, 6, 56]-code), using construction X applied to AG(F,8P) ⊂ AG(F,10P) based on
- linear OA(1660, 64, F16, 55) (dual of [64, 4, 56]-code), using algebraic-geometric code AG(F,8P) 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(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(1660, 66, F16, 54) (dual of [66, 6, 55]-code) | [i] | Truncation | |
| 2 | Linear OA(16128, 134, F16, 111) (dual of [134, 6, 112]-code) | [i] | Repeating Each Code Word | |
| 3 | Linear OA(16126, 132, F16, 110) (dual of [132, 6, 111]-code) | [i] | Juxtaposition | |
| 4 | Linear OOA(1661, 33, F16, 2, 55) (dual of [(33, 2), 5, 56]-NRT-code) | [i] | OOA Folding | |