Information on Result #676599
Linear OA(3131, 742, F3, 33) (dual of [742, 611, 34]-code), using construction X applied to Ce(33) ⊂ Ce(30) based on
- linear OA(3130, 729, F3, 34) (dual of [729, 599, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(3118, 729, F3, 31) (dual of [729, 611, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(31, 13, F3, 1) (dual of [13, 12, 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 OOA(3131, 595, F3, 2, 33) (dual of [(595, 2), 1059, 34]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3131, 595, F3, 3, 33) (dual of [(595, 3), 1654, 34]-NRT-code) | [i] | ||
| 3 | Linear OOA(3131, 595, F3, 4, 33) (dual of [(595, 4), 2249, 34]-NRT-code) | [i] | ||
| 4 | Linear OOA(3131, 595, F3, 5, 33) (dual of [(595, 5), 2844, 34]-NRT-code) | [i] | ||
| 5 | Digital (98, 131, 595)-net over F3 | [i] | ||
| 6 | Linear OOA(3131, 371, F3, 2, 33) (dual of [(371, 2), 611, 34]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(3131, 247, F3, 3, 33) (dual of [(247, 3), 610, 34]-NRT-code) | [i] | ||