Information on Result #636767
Linear OA(4136, 175, F4, 68) (dual of [175, 39, 69]-code), using concatenation of two codes based on
- linear OA(6422, 35, F64, 22) (dual of [35, 13, 23]-code or 35-arc in PG(21,64)), using
- discarding factors / shortening the dual code based on linear OA(6422, 64, F64, 22) (dual of [64, 42, 23]-code or 64-arc in PG(21,64)), using
- Reed–Solomon code RS(42,64) [i]
- discarding factors / shortening the dual code based on linear OA(6422, 64, F64, 22) (dual of [64, 42, 23]-code or 64-arc in PG(21,64)), using
- linear OA(42, 5, F4, 2) (dual of [5, 3, 3]-code or 5-arc in PG(1,4)), using
- extended Reed–Solomon code RSe(3,4) [i]
- Hamming code H(2,4) [i]
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(4136, 175, F4, 67) (dual of [175, 39, 68]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(4137, 176, F4, 68) (dual of [176, 39, 69]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(4135, 174, F4, 67) (dual of [174, 39, 68]-code) | [i] | Truncation | |
| 4 | Linear OA(4134, 173, F4, 66) (dual of [173, 39, 67]-code) | [i] | ||
| 5 | Linear OOA(4136, 87, F4, 2, 68) (dual of [(87, 2), 38, 69]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(4136, 58, F4, 3, 68) (dual of [(58, 3), 38, 69]-NRT-code) | [i] | ||