Information on Result #675956
Linear OA(3142, 2202, F3, 30) (dual of [2202, 2060, 31]-code), using construction X applied to Ce(30) ⊂ Ce(27) 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(31, 15, F3, 1) (dual of [15, 14, 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
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(3143, 2203, F3, 30) (dual of [2203, 2060, 31]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(3142, 1402, F3, 2, 30) (dual of [(1402, 2), 2662, 31]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(3142, 1402, F3, 3, 30) (dual of [(1402, 3), 4064, 31]-NRT-code) | [i] | ||
| 4 | Linear OOA(3142, 1402, F3, 4, 30) (dual of [(1402, 4), 5466, 31]-NRT-code) | [i] | ||
| 5 | Linear OOA(3142, 1402, F3, 5, 30) (dual of [(1402, 5), 6868, 31]-NRT-code) | [i] | ||
| 6 | Digital (112, 142, 1402)-net over F3 | [i] | ||
| 7 | Linear OOA(3142, 1101, F3, 2, 30) (dual of [(1101, 2), 2060, 31]-NRT-code) | [i] | OOA Folding | |
| 8 | Linear OOA(3142, 734, F3, 3, 30) (dual of [(734, 3), 2060, 31]-NRT-code) | [i] | ||
| 9 | Linear OOA(3142, 550, F3, 4, 30) (dual of [(550, 4), 2058, 31]-NRT-code) | [i] | ||
| 10 | Linear OOA(3142, 440, F3, 5, 30) (dual of [(440, 5), 2058, 31]-NRT-code) | [i] | ||