Information on Result #628255
Linear OA(712, 100, F7, 6) (dual of [100, 88, 7]-code), using trace code based on linear OA(496, 50, F49, 6) (dual of [50, 44, 7]-code or 50-arc in PG(5,49)), using
- extended Reed–Solomon code RSe(44,49) [i]
- algebraic-geometric code AG(F, Q+20P) with degQ = 3 and degPÂ =Â 2 [i] based on function field F/F49 with g(F) = 0 and N(F) ≥ 50, using the rational function field F49(x) [i]
- algebraic-geometric code AG(F, Q+13P) with degQ = 4 and degPÂ =Â 3 [i] based on function field F/F49 with g(F) = 0 and N(F) ≥ 50 (see above)
- algebraic-geometric code AG(F, Q+8P) with degQ = 3 and degPÂ =Â 5 [i] based on function field F/F49 with g(F) = 0 and N(F) ≥ 50 (see above)
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.
Compare with Markus Grassl’s online database of code parameters.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OA(713, 101, F7, 6) (dual of [101, 88, 7]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(713, 103, F7, 6) (dual of [103, 90, 7]-code) | [i] | Varšamov–Edel Lengthening | |
| 3 | Linear OA(7104, 823597, F7, 16) (dual of [823597, 823493, 17]-code) | [i] | Construction X with Extended Narrow-Sense BCH Codes | |
| 4 | Linear OA(713, 102, F7, 6) (dual of [102, 89, 7]-code) | [i] | Construction X with Varšamov Bound | |
| 5 | Linear OOA(712, 50, F7, 2, 6) (dual of [(50, 2), 88, 7]-NRT-code) | [i] | OOA Folding | |