Information on Result #634294
Linear OA(4138, 180, F4, 67) (dual of [180, 42, 68]-code), using concatenation of two codes based on
- linear OA(1639, 60, F16, 33) (dual of [60, 21, 34]-code), using
- discarding factors / shortening the dual code based on linear OA(1639, 64, F16, 33) (dual of [64, 25, 34]-code), using
- algebraic-geometric code AG(F,30P) [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- the Hermitian function field over F16 [i]
- algebraic-geometric code AG(F,30P) [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- discarding factors / shortening the dual code based on linear OA(1639, 64, F16, 33) (dual of [64, 25, 34]-code), using
- linear OA(41, 3, F4, 1) (dual of [3, 2, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(41, s, F4, 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(4137, 179, F4, 66) (dual of [179, 42, 67]-code) | [i] | Truncation | |
| 2 | Linear OOA(4138, 90, F4, 2, 67) (dual of [(90, 2), 42, 68]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(4138, 60, F4, 3, 67) (dual of [(60, 3), 42, 68]-NRT-code) | [i] | ||