Information on Result #631696
Linear OA(3107, 164, F3, 41) (dual of [164, 57, 42]-code), using concatenation of two codes based on
- linear OA(2722, 41, F27, 20) (dual of [41, 19, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(2722, 48, F27, 20) (dual of [48, 26, 21]-code), using
- extended algebraic-geometric code AGe(F,27P) [i] based on function field F/F27 with g(F) = 2 and N(F) ≥ 48, using
- discarding factors / shortening the dual code based on linear OA(2722, 48, F27, 20) (dual of [48, 26, 21]-code), using
- linear OA(31, 4, F3, 1) (dual of [4, 3, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 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(3106, 163, F3, 40) (dual of [163, 57, 41]-code) | [i] | Truncation | |
| 2 | Linear OOA(3107, 82, F3, 2, 41) (dual of [(82, 2), 57, 42]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(3107, 54, F3, 3, 41) (dual of [(54, 3), 55, 42]-NRT-code) | [i] | ||