Information on Result #695165
Linear OA(2721, 19694, F27, 7) (dual of [19694, 19673, 8]-code), using construction X applied to Ce(6) ⊂ Ce(3) based on
- linear OA(2719, 19683, F27, 7) (dual of [19683, 19664, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(2710, 19683, F27, 4) (dual of [19683, 19673, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(272, 11, F27, 2) (dual of [11, 9, 3]-code or 11-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(2721, 19694, F27, 2, 7) (dual of [(19694, 2), 39367, 8]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (14, 21, 19694)-net over F27 | [i] | ||
| 3 | Linear OOA(2721, 9847, F27, 2, 7) (dual of [(9847, 2), 19673, 8]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(2721, 6564, F27, 7, 7) (dual of [(6564, 7), 45927, 8]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |