Information on Result #2266101
Linear OA(3139, 2227, F3, 28) (dual of [2227, 2088, 29]-code), using 2 times code embedding in larger space based on linear OA(3137, 2225, F3, 28) (dual of [2225, 2088, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(21) [i] based on
- linear OA(3127, 2187, F3, 28) (dual of [2187, 2060, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(399, 2187, F3, 22) (dual of [2187, 2088, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(310, 38, F3, 5) (dual of [38, 28, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(310, 39, F3, 5) (dual of [39, 29, 6]-code), 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(3139, 1773, F3, 2, 28) (dual of [(1773, 2), 3407, 29]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3139, 1773, F3, 3, 28) (dual of [(1773, 3), 5180, 29]-NRT-code) | [i] | ||
| 3 | Linear OOA(3139, 1773, F3, 4, 28) (dual of [(1773, 4), 6953, 29]-NRT-code) | [i] | ||
| 4 | Linear OOA(3139, 1773, F3, 5, 28) (dual of [(1773, 5), 8726, 29]-NRT-code) | [i] | ||
| 5 | Digital (111, 139, 1773)-net over F3 | [i] | ||