Information on Result #694862
Linear OA(2731, 531455, F27, 8) (dual of [531455, 531424, 9]-code), using construction X applied to Ce(7) ⊂ Ce(4) based on
- linear OA(2729, 531441, F27, 8) (dual of [531441, 531412, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 531440 = 274−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(2717, 531441, F27, 5) (dual of [531441, 531424, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 531440 = 274−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(272, 14, F27, 2) (dual of [14, 12, 3]-code or 14-arc in PG(1,27)), using
- discarding factors / shortening the dual code based on linear OA(272, 27, F27, 2) (dual of [27, 25, 3]-code or 27-arc in PG(1,27)), using
- Reed–Solomon code RS(25,27) [i]
- discarding factors / shortening the dual code based on linear OA(272, 27, F27, 2) (dual of [27, 25, 3]-code or 27-arc in PG(1,27)), 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.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(2731, 531455, F27, 2, 8) (dual of [(531455, 2), 1062879, 9]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (23, 31, 531455)-net over F27 | [i] | ||
| 3 | Linear OOA(2731, 265727, F27, 2, 8) (dual of [(265727, 2), 531423, 9]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(2731, 132863, F27, 8, 8) (dual of [(132863, 8), 1062873, 9]-NRT-code) | [i] | OA Folding and Stacking | |