Information on Result #675962
Linear OA(3131, 2205, F3, 28) (dual of [2205, 2074, 29]-code), using construction X applied to Ce(27) ⊂ Ce(24) 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(3113, 2187, F3, 25) (dual of [2187, 2074, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(34, 18, F3, 2) (dual of [18, 14, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(34, 40, F3, 2) (dual of [40, 36, 3]-code), using
- Hamming code H(4,3) [i]
- discarding factors / shortening the dual code based on linear OA(34, 40, F3, 2) (dual of [40, 36, 3]-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 OA(3132, 2206, F3, 28) (dual of [2206, 2074, 29]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(3131, 1258, F3, 2, 28) (dual of [(1258, 2), 2385, 29]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(3131, 1258, F3, 3, 28) (dual of [(1258, 3), 3643, 29]-NRT-code) | [i] | ||
| 4 | Linear OOA(3131, 1258, F3, 4, 28) (dual of [(1258, 4), 4901, 29]-NRT-code) | [i] | ||
| 5 | Linear OOA(3131, 1258, F3, 5, 28) (dual of [(1258, 5), 6159, 29]-NRT-code) | [i] | ||
| 6 | Digital (103, 131, 1258)-net over F3 | [i] | ||
| 7 | Linear OOA(3131, 1102, F3, 2, 28) (dual of [(1102, 2), 2073, 29]-NRT-code) | [i] | OOA Folding | |
| 8 | Linear OOA(3131, 735, F3, 3, 28) (dual of [(735, 3), 2074, 29]-NRT-code) | [i] | ||
| 9 | Linear OOA(3131, 551, F3, 4, 28) (dual of [(551, 4), 2073, 29]-NRT-code) | [i] | ||
| 10 | Linear OOA(3131, 441, F3, 5, 28) (dual of [(441, 5), 2074, 29]-NRT-code) | [i] | ||