Information on Result #676200
Linear OA(3143, 2197, F3, 31) (dual of [2197, 2054, 32]-code), using construction XX applied to Ce(30) ⊂ Ce(28) ⊂ 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(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(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, 9, F3, 1) (dual of [9, 8, 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(30, 1, F3, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [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(3143, 1239, F3, 2, 31) (dual of [(1239, 2), 2335, 32]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3143, 1239, F3, 3, 31) (dual of [(1239, 3), 3574, 32]-NRT-code) | [i] | ||
| 3 | Linear OOA(3143, 1239, F3, 4, 31) (dual of [(1239, 4), 4813, 32]-NRT-code) | [i] | ||
| 4 | Linear OOA(3143, 1239, F3, 5, 31) (dual of [(1239, 5), 6052, 32]-NRT-code) | [i] | ||
| 5 | Digital (112, 143, 1239)-net over F3 | [i] | ||
| 6 | Linear OOA(3143, 1098, F3, 2, 31) (dual of [(1098, 2), 2053, 32]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(3143, 732, F3, 3, 31) (dual of [(732, 3), 2053, 32]-NRT-code) | [i] | ||
| 8 | Linear OOA(3143, 549, F3, 4, 31) (dual of [(549, 4), 2053, 32]-NRT-code) | [i] | ||