Information on Result #637593
Linear OA(554, 78, F5, 29) (dual of [78, 24, 30]-code), using concatenation of two codes based on
- linear OA(2514, 26, F25, 14) (dual of [26, 12, 15]-code or 26-arc in PG(13,25)), using
- extended Reed–Solomon code RSe(12,25) [i]
- algebraic-geometric code AG(F, Q+4P) with degQ = 3 and degPÂ =Â 2 [i] based on function field F/F25 with g(F) = 0 and N(F) ≥ 26, using the rational function field F25(x) [i]
- algebraic-geometric code AG(F, Q+3P) with degQ = 2 and degPÂ =Â 3 [i] based on function field F/F25 with g(F) = 0 and N(F) ≥ 26 (see above)
- linear OA(51, 3, F5, 1) (dual of [3, 2, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(51, s, F5, 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.
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(554, 78, F5, 28) (dual of [78, 24, 29]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(555, 79, F5, 29) (dual of [79, 24, 30]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(556, 80, F5, 29) (dual of [80, 24, 30]-code) | [i] | ||
| 4 | Linear OA(557, 81, F5, 29) (dual of [81, 24, 30]-code) | [i] | ||
| 5 | Linear OA(553, 77, F5, 28) (dual of [77, 24, 29]-code) | [i] | Truncation | |
| 6 | Linear OOA(554, 39, F5, 2, 29) (dual of [(39, 2), 24, 30]-NRT-code) | [i] | OOA Folding | |