Information on Result #629752
Linear OA(2138, 210, F2, 41) (dual of [210, 72, 42]-code), using concatenation of two codes based on
- linear OA(1624, 42, F16, 20) (dual of [42, 18, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(1624, 45, F16, 20) (dual of [45, 21, 21]-code), using
- extended algebraic-geometric code AGe(F,24P) [i] based on function field F/F16 with g(F) = 4 and N(F) ≥ 45, using
- discarding factors / shortening the dual code based on linear OA(1624, 45, F16, 20) (dual of [45, 21, 21]-code), using
- linear OA(21, 5, F2, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(21, s, F2, 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(2137, 209, F2, 40) (dual of [209, 72, 41]-code) | [i] | Truncation | |
| 2 | Linear OOA(2138, 105, F2, 2, 41) (dual of [(105, 2), 72, 42]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(2138, 70, F2, 3, 41) (dual of [(70, 3), 72, 42]-NRT-code) | [i] | ||