Information on Result #676193
Linear OA(3159, 2207, F3, 33) (dual of [2207, 2048, 34]-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(31, 17, F3, 1) (dual of [17, 16, 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, 3, F3, 1) (dual of [3, 2, 2]-code), using
- Reed–Solomon code RS(2,3) [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(3159, 1649, F3, 2, 33) (dual of [(1649, 2), 3139, 34]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3159, 1649, F3, 3, 33) (dual of [(1649, 3), 4788, 34]-NRT-code) | [i] | ||
| 3 | Linear OOA(3159, 1649, F3, 4, 33) (dual of [(1649, 4), 6437, 34]-NRT-code) | [i] | ||
| 4 | Linear OOA(3159, 1649, F3, 5, 33) (dual of [(1649, 5), 8086, 34]-NRT-code) | [i] | ||
| 5 | Digital (126, 159, 1649)-net over F3 | [i] | ||