Information on Result #636701
Linear OA(4115, 160, F4, 53) (dual of [160, 45, 54]-code), using concatenation of two codes based on
- linear OA(6417, 32, F64, 17) (dual of [32, 15, 18]-code or 32-arc in PG(16,64)), using
- discarding factors / shortening the dual code based on linear OA(6417, 64, F64, 17) (dual of [64, 47, 18]-code or 64-arc in PG(16,64)), using
- Reed–Solomon code RS(47,64) [i]
- discarding factors / shortening the dual code based on linear OA(6417, 64, F64, 17) (dual of [64, 47, 18]-code or 64-arc in PG(16,64)), 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(4115, 160, F4, 52) (dual of [160, 45, 53]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(4116, 161, F4, 53) (dual of [161, 45, 54]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(4114, 159, F4, 52) (dual of [159, 45, 53]-code) | [i] | Truncation | |
| 4 | Linear OA(4113, 158, F4, 51) (dual of [158, 45, 52]-code) | [i] | ||
| 5 | Linear OOA(4115, 80, F4, 2, 53) (dual of [(80, 2), 45, 54]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(4115, 53, F4, 3, 53) (dual of [(53, 3), 44, 54]-NRT-code) | [i] | ||