Information on Result #636700
Linear OA(4117, 165, F4, 53) (dual of [165, 48, 54]-code), using concatenation of two codes based on
- linear OA(6417, 33, F64, 17) (dual of [33, 16, 18]-code or 33-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(4117, 165, F4, 52) (dual of [165, 48, 53]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(4118, 166, F4, 53) (dual of [166, 48, 54]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(4116, 164, F4, 52) (dual of [164, 48, 53]-code) | [i] | Truncation | |
| 4 | Linear OA(4115, 163, F4, 51) (dual of [163, 48, 52]-code) | [i] | ||
| 5 | Linear OOA(4117, 82, F4, 2, 53) (dual of [(82, 2), 47, 54]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(4117, 55, F4, 3, 53) (dual of [(55, 3), 48, 54]-NRT-code) | [i] | ||