Information on Result #637587
Linear OA(552, 78, F5, 27) (dual of [78, 26, 28]-code), using concatenation of two codes based on
- linear OA(2513, 26, F25, 13) (dual of [26, 13, 14]-code or 26-arc in PG(12,25)), using
- extended Reed–Solomon code RSe(13,25) [i]
- the expurgated narrow-sense BCH-code C(I) with length 26 | 252−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- algebraic-geometric code AG(F,6P) with 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,4P) with 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(552, 78, F5, 26) (dual of [78, 26, 27]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(553, 79, F5, 27) (dual of [79, 26, 28]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(554, 80, F5, 27) (dual of [80, 26, 28]-code) | [i] | ||
| 4 | Linear OA(555, 81, F5, 27) (dual of [81, 26, 28]-code) | [i] | ||
| 5 | Linear OA(551, 77, F5, 26) (dual of [77, 26, 27]-code) | [i] | Truncation | |
| 6 | Linear OOA(552, 39, F5, 2, 27) (dual of [(39, 2), 26, 28]-NRT-code) | [i] | OOA Folding | |