Information on Result #661536
Linear OA(565, 87, F5, 35) (dual of [87, 22, 36]-code), using concatenation of two codes based on
- linear OA(2518, 29, F25, 17) (dual of [29, 11, 18]-code), using
- construction X applied to AG(F,4P) ⊂ AG(F,5P) [i] based on
- linear OA(2517, 26, F25, 17) (dual of [26, 9, 18]-code or 26-arc in PG(16,25)), using 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]
- linear OA(2515, 26, F25, 15) (dual of [26, 11, 16]-code or 26-arc in PG(14,25)), using algebraic-geometric code AG(F,5P) with degPÂ =Â 2 [i] based on function field F/F25 with g(F) = 0 and N(F) ≥ 26 (see above)
- linear OA(251, 3, F25, 1) (dual of [3, 2, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(251, s, F25, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to AG(F,4P) ⊂ AG(F,5P) [i] based on
- 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(565, 87, F5, 34) (dual of [87, 22, 35]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(564, 86, F5, 34) (dual of [86, 22, 35]-code) | [i] | Truncation | |
| 3 | Linear OOA(565, 43, F5, 2, 35) (dual of [(43, 2), 21, 36]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(565, 29, F5, 3, 35) (dual of [(29, 3), 22, 36]-NRT-code) | [i] | ||