Information on Result #662675
Linear OA(513, 30, F5, 7) (dual of [30, 17, 8]-code), using generalized (u, u+v)-construction based on
- linear OA(51, 6, F5, 1) (dual of [6, 5, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(51, s, F5, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- linear OA(51, 6, F5, 1) (dual of [6, 5, 2]-code) (see above)
- linear OA(52, 6, F5, 2) (dual of [6, 4, 3]-code or 6-arc in PG(1,5)), using
- extended Reed–Solomon code RSe(4,5) [i]
- Hamming code H(2,5) [i]
- linear OA(53, 6, F5, 3) (dual of [6, 3, 4]-code or 6-arc in PG(2,5) or 6-cap in PG(2,5)), using
- extended Reed–Solomon code RSe(3,5) [i]
- oval in PG(2, 5) [i]
- linear OA(56, 6, F5, 6) (dual of [6, 0, 7]-code or 6-arc in PG(5,5)), 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(590, 154, F5, 39) (dual of [154, 64, 40]-code) | [i] | Construction X with Extended Narrow-Sense BCH Codes | |
| 2 | Linear OA(5104, 157, F5, 46) (dual of [157, 53, 47]-code) | [i] | Construction XX with a Chain of Extended Narrow-Sense BCH Codes | |