Information on Result #661741
Linear OA(1697, 104, F16, 82) (dual of [104, 7, 83]-code), using juxtaposition based on
- linear OA(1631, 38, F16, 28) (dual of [38, 7, 29]-code), using
- extended algebraic-geometric code AGe(F,9P) [i] based on function field F/F16 with g(F) = 3 and N(F) ≥ 38, using
- linear OA(1659, 66, F16, 53) (dual of [66, 7, 54]-code), using
- construction X applied to AG(F,10P) ⊂ AG(F,12P) [i] based on
- 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, using the Hermitian function field over F16 [i]
- linear OA(1657, 64, F16, 51) (dual of [64, 7, 52]-code), using algebraic-geometric code AG(F,12P) [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65 (see above)
- linear OA(161, 2, F16, 1) (dual of [2, 1, 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
- construction X applied to AG(F,10P) ⊂ AG(F,12P) [i] based on
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(1697, 104, F16, 81) (dual of [104, 7, 82]-code) | [i] | Strength Reduction | |
| 2 | Linear OOA(1697, 52, F16, 2, 82) (dual of [(52, 2), 7, 83]-NRT-code) | [i] | OOA Folding | |