Information on Result #694829
Linear OA(2778, 531450, F27, 20) (dual of [531450, 531372, 21]-code), using construction X applied to Ce(19) ⊂ Ce(17) based on
- linear OA(2777, 531441, F27, 20) (dual of [531441, 531364, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 531440 = 274−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(2769, 531441, F27, 18) (dual of [531441, 531372, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 531440 = 274−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(271, 9, F27, 1) (dual of [9, 8, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(271, s, F27, 1) (dual of [s, s−1, 2]-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 OA(2790, 531498, F27, 20) (dual of [531498, 531408, 21]-code) | [i] | (u, u+v)-Construction | |
| 2 | Linear OA(2792, 531514, F27, 20) (dual of [531514, 531422, 21]-code) | [i] | ||
| 3 | OA(2794, 531566, S27, 20) | [i] | ||
| 4 | Linear OOA(2778, 385659, F27, 2, 20) (dual of [(385659, 2), 771240, 21]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 5 | Digital (58, 78, 385659)-net over F27 | [i] | ||
| 6 | Linear OOA(2778, 265725, F27, 2, 20) (dual of [(265725, 2), 531372, 21]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(2778, 53145, F27, 20, 20) (dual of [(53145, 20), 1062822, 21]-NRT-code) | [i] | OA Folding and Stacking | |