Information on Result #676194
Linear OA(3161, 2208, F3, 34) (dual of [2208, 2047, 35]-code), using construction XX applied to Ce(33) ⊂ Ce(30) ⊂ Ce(28) based on
- linear OA(3155, 2187, F3, 34) (dual of [2187, 2032, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(3141, 2187, F3, 31) (dual of [2187, 2046, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- 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(34, 19, F3, 2) (dual of [19, 15, 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
- linear OA(31, 2, F3, 1) (dual of [2, 1, 2]-code), using
- dual of repetition code with length 2 [i]
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(3161, 1525, F3, 2, 34) (dual of [(1525, 2), 2889, 35]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3161, 1525, F3, 3, 34) (dual of [(1525, 3), 4414, 35]-NRT-code) | [i] | ||
| 3 | Linear OOA(3161, 1525, F3, 4, 34) (dual of [(1525, 4), 5939, 35]-NRT-code) | [i] | ||
| 4 | Linear OOA(3161, 1525, F3, 5, 34) (dual of [(1525, 5), 7464, 35]-NRT-code) | [i] | ||
| 5 | Digital (127, 161, 1525)-net over F3 | [i] | ||
| 6 | Linear OOA(3161, 1104, F3, 2, 34) (dual of [(1104, 2), 2047, 35]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(3161, 736, F3, 3, 34) (dual of [(736, 3), 2047, 35]-NRT-code) | [i] | ||
| 8 | Linear OOA(3161, 552, F3, 4, 34) (dual of [(552, 4), 2047, 35]-NRT-code) | [i] | ||