Information on Result #636750
Linear OA(4135, 180, F4, 65) (dual of [180, 45, 66]-code), using concatenation of two codes based on
- linear OA(6421, 36, F64, 21) (dual of [36, 15, 22]-code or 36-arc in PG(20,64)), using
- discarding factors / shortening the dual code based on linear OA(6421, 64, F64, 21) (dual of [64, 43, 22]-code or 64-arc in PG(20,64)), using
- Reed–Solomon code RS(43,64) [i]
- discarding factors / shortening the dual code based on linear OA(6421, 64, F64, 21) (dual of [64, 43, 22]-code or 64-arc in PG(20,64)), 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(4135, 180, F4, 64) (dual of [180, 45, 65]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(4136, 181, F4, 65) (dual of [181, 45, 66]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(4134, 179, F4, 64) (dual of [179, 45, 65]-code) | [i] | Truncation | |
| 4 | Linear OA(4133, 178, F4, 63) (dual of [178, 45, 64]-code) | [i] | ||
| 5 | Linear OOA(4135, 90, F4, 2, 65) (dual of [(90, 2), 45, 66]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(4135, 60, F4, 3, 65) (dual of [(60, 3), 45, 66]-NRT-code) | [i] | ||