Information on Result #628285
Linear OA(742, 100, F7, 21) (dual of [100, 58, 22]-code), using trace code based on linear OA(4921, 50, F49, 21) (dual of [50, 29, 22]-code or 50-arc in PG(20,49)), using
- extended Reed–Solomon code RSe(29,49) [i]
- the expurgated narrow-sense BCH-code C(I) with length 50 | 492−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- algebraic-geometric code AG(F,14P) with 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+8P) 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+5P) 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(743, 101, F7, 21) (dual of [101, 58, 22]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(743, 103, F7, 21) (dual of [103, 60, 22]-code) | [i] | Varšamov–Edel Lengthening | |
| 3 | Linear OA(743, 102, F7, 21) (dual of [102, 59, 22]-code) | [i] | Construction X with Varšamov Bound | |
| 4 | Linear OOA(742, 50, F7, 2, 21) (dual of [(50, 2), 58, 22]-NRT-code) | [i] | OOA Folding | |