Information on Result #695106
Linear OA(2713, 19686, F27, 5) (dual of [19686, 19673, 6]-code), using construction X applied to Ce(4) ⊂ Ce(3) based on
- linear OA(2713, 19683, F27, 5) (dual of [19683, 19670, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [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(270, 3, F27, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(270, s, F27, 0) (dual of [s, s, 1]-code) for arbitrarily large s, 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(2713, 19686, F27, 2, 5) (dual of [(19686, 2), 39359, 6]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (8, 13, 19686)-net over F27 | [i] | ||
| 3 | Linear OOA(2713, 9843, F27, 2, 5) (dual of [(9843, 2), 19673, 6]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(2713, 9842, F27, 5, 5) (dual of [(9842, 5), 49197, 6]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |