Information on Result #661546
Linear OA(5150, 210, F5, 69) (dual of [210, 60, 70]-code), using concatenation of two codes based on
- linear OA(2540, 70, F25, 34) (dual of [70, 30, 35]-code), using
- construction X applied to AG(F,30P) ⊂ AG(F,33P) [i] based on
- linear OA(2538, 65, F25, 34) (dual of [65, 27, 35]-code), using algebraic-geometric code AG(F,30P) [i] based on function field F/F25 with g(F) = 4 and N(F) ≥ 66, using
- linear OA(2535, 65, F25, 31) (dual of [65, 30, 32]-code), using algebraic-geometric code AG(F,33P) [i] based on function field F/F25 with g(F) = 4 and N(F) ≥ 66 (see above)
- linear OA(252, 5, F25, 2) (dual of [5, 3, 3]-code or 5-arc in PG(1,25)), using
- discarding factors / shortening the dual code based on linear OA(252, 25, F25, 2) (dual of [25, 23, 3]-code or 25-arc in PG(1,25)), using
- Reed–Solomon code RS(23,25) [i]
- discarding factors / shortening the dual code based on linear OA(252, 25, F25, 2) (dual of [25, 23, 3]-code or 25-arc in PG(1,25)), using
- construction X applied to AG(F,30P) ⊂ AG(F,33P) [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.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OA(5150, 210, F5, 68) (dual of [210, 60, 69]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(5149, 209, F5, 68) (dual of [209, 60, 69]-code) | [i] | Truncation | |
| 3 | Linear OOA(5150, 105, F5, 2, 69) (dual of [(105, 2), 60, 70]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(5150, 70, F5, 3, 69) (dual of [(70, 3), 60, 70]-NRT-code) | [i] | ||