Information on Result #1013703
Linear OOA(753, 3843210, F7, 3, 7) (dual of [(3843210, 3), 11529577, 8]-NRT-code), using (u, u+v)-construction based on
- linear OOA(73, 8, F7, 3, 3) (dual of [(8, 3), 21, 4]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(3;21,7) [i]
- linear OOA(750, 3843202, F7, 3, 7) (dual of [(3843202, 3), 11529556, 8]-NRT-code), using
- trace code [i] based on linear OOA(4925, 1921601, F49, 3, 7) (dual of [(1921601, 3), 5764778, 8]-NRT-code), using
- OOA 3-folding [i] based on linear OA(4925, 5764803, F49, 7) (dual of [5764803, 5764778, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(4925, 5764805, F49, 7) (dual of [5764805, 5764780, 8]-code), using
- construction X applied to Ce(6) ⊂ Ce(5) [i] based on
- linear OA(4925, 5764801, F49, 7) (dual of [5764801, 5764776, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(4921, 5764801, F49, 6) (dual of [5764801, 5764780, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(490, 4, F49, 0) (dual of [4, 4, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(490, s, F49, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(6) ⊂ Ce(5) [i] based on
- discarding factors / shortening the dual code based on linear OA(4925, 5764805, F49, 7) (dual of [5764805, 5764780, 8]-code), using
- OOA 3-folding [i] based on linear OA(4925, 5764803, F49, 7) (dual of [5764803, 5764778, 8]-code), using
- trace code [i] based on linear OOA(4925, 1921601, F49, 3, 7) (dual of [(1921601, 3), 5764778, 8]-NRT-code), using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m and t.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(766, 7686420, F7, 3, 7) (dual of [(7686420, 3), 23059194, 8]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |
| 2 | Linear OOA(753, 3843209, F7, 9, 7) (dual of [(3843209, 9), 34588828, 8]-NRT-code) | [i] | OOA Stacking with Additional Row | |