Information on Result #638616
Linear OA(780, 90, F7, 55) (dual of [90, 10, 56]-code), using concatenation of two codes based on
- linear OA(4913, 18, F49, 13) (dual of [18, 5, 14]-code or 18-arc in PG(12,49)), using
- discarding factors / shortening the dual code based on linear OA(4913, 49, F49, 13) (dual of [49, 36, 14]-code or 49-arc in PG(12,49)), using
- Reed–Solomon code RS(36,49) [i]
- discarding factors / shortening the dual code based on linear OA(4913, 49, F49, 13) (dual of [49, 36, 14]-code or 49-arc in PG(12,49)), using
- 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
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(780, 90, F7, 54) (dual of [90, 10, 55]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(779, 89, F7, 54) (dual of [89, 10, 55]-code) | [i] | Truncation | |
| 3 | Linear OA(777, 87, F7, 52) (dual of [87, 10, 53]-code) | [i] | ||
| 4 | Linear OA(776, 86, F7, 51) (dual of [86, 10, 52]-code) | [i] | ||
| 5 | Linear OA(773, 83, F7, 48) (dual of [83, 10, 49]-code) | [i] | ||
| 6 | Linear OOA(780, 45, F7, 2, 55) (dual of [(45, 2), 10, 56]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(780, 30, F7, 3, 55) (dual of [(30, 3), 10, 56]-NRT-code) | [i] | ||