Information on Result #638454
Linear OA(7106, 150, F7, 57) (dual of [150, 44, 58]-code), using concatenation of two codes based on
- linear OA(4928, 50, F49, 28) (dual of [50, 22, 29]-code or 50-arc in PG(27,49)), using
- extended Reed–Solomon code RSe(22,49) [i]
- algebraic-geometric code AG(F, Q+9P) 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,7P) 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+3P) with degQ = 6 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(7106, 150, F7, 56) (dual of [150, 44, 57]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(7107, 151, F7, 57) (dual of [151, 44, 58]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(7108, 152, F7, 57) (dual of [152, 44, 58]-code) | [i] | ||
| 4 | Linear OA(7105, 149, F7, 56) (dual of [149, 44, 57]-code) | [i] | Truncation | |
| 5 | Linear OOA(7106, 75, F7, 2, 57) (dual of [(75, 2), 44, 58]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(7106, 50, F7, 3, 57) (dual of [(50, 3), 44, 58]-NRT-code) | [i] | ||