Information on Result #663146
Linear OA(721, 30, F7, 14) (dual of [30, 9, 15]-code), using generalized (u, u+v)-construction based on
- linear OA(72, 5, F7, 2) (dual of [5, 3, 3]-code or 5-arc in PG(1,7)), using
- discarding factors / shortening the dual code based on linear OA(72, 7, F7, 2) (dual of [7, 5, 3]-code or 7-arc in PG(1,7)), using
- Reed–Solomon code RS(5,7) [i]
- discarding factors / shortening the dual code based on linear OA(72, 7, F7, 2) (dual of [7, 5, 3]-code or 7-arc in PG(1,7)), using
- linear OA(72, 5, F7, 2) (dual of [5, 3, 3]-code or 5-arc in PG(1,7)) (see above)
- linear OA(73, 5, F7, 3) (dual of [5, 2, 4]-code or 5-arc in PG(2,7) or 5-cap in PG(2,7)), using
- discarding factors / shortening the dual code based on linear OA(73, 7, F7, 3) (dual of [7, 4, 4]-code or 7-arc in PG(2,7) or 7-cap in PG(2,7)), using
- Reed–Solomon code RS(4,7) [i]
- discarding factors / shortening the dual code based on linear OA(73, 7, F7, 3) (dual of [7, 4, 4]-code or 7-arc in PG(2,7) or 7-cap in PG(2,7)), using
- linear OA(74, 5, F7, 4) (dual of [5, 1, 5]-code or 5-arc in PG(3,7)), using
- dual of repetition code with length 5 [i]
- linear OA(75, 5, F7, 5) (dual of [5, 0, 6]-code or 5-arc in PG(4,7)), using
- linear OA(75, 5, F7, 5) (dual of [5, 0, 6]-code or 5-arc in PG(4,7)) (see above)
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(771, 80, F7, 48) (dual of [80, 9, 49]-code) | [i] | Juxtaposition | |
| 2 | Linear OA(769, 78, F7, 47) (dual of [78, 9, 48]-code) | [i] | Construction XX with a Chain of Cyclic Codes | |