Information on Result #988572
Linear OOA(4932, 1921606, F49, 3, 8) (dual of [(1921606, 3), 5764786, 9]-NRT-code), using OOA 3-folding based on linear OA(4932, 5764818, F49, 8) (dual of [5764818, 5764786, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(4932, 5764820, F49, 8) (dual of [5764820, 5764788, 9]-code), using
- construction X applied to Ce(7) ⊂ Ce(3) [i] based on
- linear OA(4929, 5764801, F49, 8) (dual of [5764801, 5764772, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(4913, 5764801, F49, 4) (dual of [5764801, 5764788, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(493, 19, F49, 3) (dual of [19, 16, 4]-code or 19-arc in PG(2,49) or 19-cap in PG(2,49)), using
- discarding factors / shortening the dual code based on linear OA(493, 49, F49, 3) (dual of [49, 46, 4]-code or 49-arc in PG(2,49) or 49-cap in PG(2,49)), using
- Reed–Solomon code RS(46,49) [i]
- discarding factors / shortening the dual code based on linear OA(493, 49, F49, 3) (dual of [49, 46, 4]-code or 49-arc in PG(2,49) or 49-cap in PG(2,49)), using
- construction X applied to Ce(7) ⊂ Ce(3) [i] based on
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.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(764, 3843212, F7, 3, 8) (dual of [(3843212, 3), 11529572, 9]-NRT-code) | [i] | Trace Code for OOAs | |
| 2 | Linear OOA(4945, 3843212, F49, 3, 8) (dual of [(3843212, 3), 11529591, 9]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |