Information on Result #695683
Linear OA(2731, 737, F27, 15) (dual of [737, 706, 16]-code), using construction X applied to Ce(14) ⊂ Ce(11) based on
- linear OA(2729, 729, F27, 15) (dual of [729, 700, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(2723, 729, F27, 12) (dual of [729, 706, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(272, 8, F27, 2) (dual of [8, 6, 3]-code or 8-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, 432, F27, 2, 15) (dual of [(432, 2), 833, 16]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (16, 31, 432)-net over F27 | [i] | ||
| 3 | Linear OOA(2731, 105, F27, 15, 15) (dual of [(105, 15), 1544, 16]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |