Information on Result #638026
Linear OA(586, 104, F5, 53) (dual of [104, 18, 54]-code), using concatenation of two codes based on
- linear OA(2517, 26, F25, 17) (dual of [26, 9, 18]-code or 26-arc in PG(16,25)), using
- extended Reed–Solomon code RSe(9,25) [i]
- the expurgated narrow-sense BCH-code C(I) with length 26 | 252−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- algebraic-geometric code AG(F,4P) 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, Q+2P) 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(52, 4, F5, 2) (dual of [4, 2, 3]-code or 4-arc in PG(1,5)), using
- discarding factors / shortening the dual code based on linear OA(52, 5, F5, 2) (dual of [5, 3, 3]-code or 5-arc in PG(1,5)), using
- Reed–Solomon code RS(3,5) [i]
- discarding factors / shortening the dual code based on linear OA(52, 5, F5, 2) (dual of [5, 3, 3]-code or 5-arc in PG(1,5)), 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(585, 103, F5, 52) (dual of [103, 18, 53]-code) | [i] | Truncation | |
| 2 | Linear OA(584, 102, F5, 51) (dual of [102, 18, 52]-code) | [i] | ||
| 3 | Linear OA(583, 101, F5, 50) (dual of [101, 18, 51]-code) | [i] | ||
| 4 | Linear OA(581, 99, F5, 48) (dual of [99, 18, 49]-code) | [i] | ||
| 5 | Linear OOA(586, 52, F5, 2, 53) (dual of [(52, 2), 18, 54]-NRT-code) | [i] | OOA Folding | |