Information on Result #2265667
Linear OA(3111, 2227, F3, 22) (dual of [2227, 2116, 23]-code), using 2 times code embedding in larger space based on linear OA(3109, 2225, F3, 22) (dual of [2225, 2116, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(15) [i] based on
- 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(371, 2187, F3, 16) (dual of [2187, 2116, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [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(3111, 1729, F3, 2, 22) (dual of [(1729, 2), 3347, 23]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3111, 1729, F3, 3, 22) (dual of [(1729, 3), 5076, 23]-NRT-code) | [i] | ||
| 3 | Linear OOA(3111, 1729, F3, 4, 22) (dual of [(1729, 4), 6805, 23]-NRT-code) | [i] | ||
| 4 | Linear OOA(3111, 1729, F3, 5, 22) (dual of [(1729, 5), 8534, 23]-NRT-code) | [i] | ||
| 5 | Digital (89, 111, 1729)-net over F3 | [i] | ||