Information on Result #676201
Linear OA(3146, 2209, F3, 30) (dual of [2209, 2063, 31]-code), using construction XX applied to Ce(30) ⊂ Ce(27) ⊂ Ce(25) based on
- 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(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(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(31, 18, F3, 1) (dual of [18, 17, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- linear OA(31, 4, F3, 1) (dual of [4, 3, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s (see above)
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(3146, 1644, F3, 2, 30) (dual of [(1644, 2), 3142, 31]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3146, 1644, F3, 3, 30) (dual of [(1644, 3), 4786, 31]-NRT-code) | [i] | ||
| 3 | Linear OOA(3146, 1644, F3, 4, 30) (dual of [(1644, 4), 6430, 31]-NRT-code) | [i] | ||
| 4 | Linear OOA(3146, 1644, F3, 5, 30) (dual of [(1644, 5), 8074, 31]-NRT-code) | [i] | ||
| 5 | Digital (116, 146, 1644)-net over F3 | [i] | ||
| 6 | Linear OOA(3146, 1104, F3, 2, 30) (dual of [(1104, 2), 2062, 31]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(3146, 736, F3, 3, 30) (dual of [(736, 3), 2062, 31]-NRT-code) | [i] | ||
| 8 | Linear OOA(3146, 552, F3, 4, 30) (dual of [(552, 4), 2062, 31]-NRT-code) | [i] | ||