Information on Result #675960
Linear OA(3138, 2205, F3, 29) (dual of [2205, 2067, 30]-code), using construction X applied to Ce(28) ⊂ Ce(25) based on
- linear OA(3134, 2187, F3, 29) (dual of [2187, 2053, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(3120, 2187, F3, 26) (dual of [2187, 2067, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [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 OOA(3138, 1415, F3, 2, 29) (dual of [(1415, 2), 2692, 30]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3138, 1415, F3, 3, 29) (dual of [(1415, 3), 4107, 30]-NRT-code) | [i] | ||
| 3 | Linear OOA(3138, 1415, F3, 4, 29) (dual of [(1415, 4), 5522, 30]-NRT-code) | [i] | ||
| 4 | Linear OOA(3138, 1415, F3, 5, 29) (dual of [(1415, 5), 6937, 30]-NRT-code) | [i] | ||
| 5 | Digital (109, 138, 1415)-net over F3 | [i] | ||
| 6 | Linear OOA(3138, 1102, F3, 2, 29) (dual of [(1102, 2), 2066, 30]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(3138, 735, F3, 3, 29) (dual of [(735, 3), 2067, 30]-NRT-code) | [i] | ||
| 8 | Linear OOA(3138, 551, F3, 4, 29) (dual of [(551, 4), 2066, 30]-NRT-code) | [i] | ||
| 9 | Linear OOA(3138, 441, F3, 5, 29) (dual of [(441, 5), 2067, 30]-NRT-code) | [i] | ||