Information on Result #631825
Linear OA(3136, 208, F3, 51) (dual of [208, 72, 52]-code), using concatenation of two codes based on
- linear OA(2728, 52, F27, 25) (dual of [52, 24, 26]-code), using
- extended algebraic-geometric code AGe(F,26P) [i] based on function field F/F27 with g(F) = 3 and N(F) ≥ 52, 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(3136, 208, F3, 50) (dual of [208, 72, 51]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(3137, 209, F3, 51) (dual of [209, 72, 52]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(3138, 210, F3, 51) (dual of [210, 72, 52]-code) | [i] | ||
| 4 | Linear OA(3139, 211, F3, 51) (dual of [211, 72, 52]-code) | [i] | ||
| 5 | Linear OA(3140, 212, F3, 51) (dual of [212, 72, 52]-code) | [i] | ||
| 6 | Linear OA(3135, 207, F3, 50) (dual of [207, 72, 51]-code) | [i] | Truncation | |
| 7 | Linear OOA(3136, 104, F3, 2, 51) (dual of [(104, 2), 72, 52]-NRT-code) | [i] | OOA Folding | |