Information on Result #638403
Linear OA(7100, 150, F7, 51) (dual of [150, 50, 52]-code), using concatenation of two codes based on
- linear OA(4925, 50, F49, 25) (dual of [50, 25, 26]-code or 50-arc in PG(24,49)), using
- extended Reed–Solomon code RSe(25,49) [i]
- the expurgated narrow-sense BCH-code C(I) with length 50 | 492−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- algebraic-geometric code AG(F,12P) 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,8P) with 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+4P) with degQ = 4 and degPÂ =Â 5 [i] based on function field F/F49 with g(F) = 0 and N(F) ≥ 50 (see above)
- linear OA(71, 3, F7, 1) (dual of [3, 2, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(71, s, F7, 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(7100, 150, F7, 50) (dual of [150, 50, 51]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(7101, 151, F7, 51) (dual of [151, 50, 52]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(7102, 152, F7, 51) (dual of [152, 50, 52]-code) | [i] | ||
| 4 | Linear OA(799, 149, F7, 50) (dual of [149, 50, 51]-code) | [i] | Truncation | |
| 5 | Linear OOA(7100, 75, F7, 2, 51) (dual of [(75, 2), 50, 52]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(7100, 50, F7, 3, 51) (dual of [(50, 3), 50, 52]-NRT-code) | [i] | ||