Information on Result #674784
Linear OA(3222, 59071, F3, 33) (dual of [59071, 58849, 34]-code), using construction X applied to C([0,16]) ⊂ C([0,15]) based on
- linear OA(3221, 59050, F3, 33) (dual of [59050, 58829, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 59050 | 320−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
- linear OA(3201, 59050, F3, 31) (dual of [59050, 58849, 32]-code), using the expurgated narrow-sense BCH-code C(I) with length 59050 | 320−1, defining interval I = [0,15], and minimum distance d ≥ |{−15,−14,…,15}|+1 = 32 (BCH-bound) [i]
- linear OA(31, 21, F3, 1) (dual of [21, 20, 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(3223, 59072, F3, 33) (dual of [59072, 58849, 34]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(3224, 59073, F3, 33) (dual of [59073, 58849, 34]-code) | [i] | ||
| 3 | Linear OA(3225, 59074, F3, 33) (dual of [59074, 58849, 34]-code) | [i] | ||
| 4 | Linear OOA(3222, 29535, F3, 2, 33) (dual of [(29535, 2), 58848, 34]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(3222, 19690, F3, 3, 33) (dual of [(19690, 3), 58848, 34]-NRT-code) | [i] | ||
| 6 | Linear OOA(3222, 14767, F3, 4, 33) (dual of [(14767, 4), 58846, 34]-NRT-code) | [i] | ||
| 7 | Linear OOA(3222, 11814, F3, 5, 33) (dual of [(11814, 5), 58848, 34]-NRT-code) | [i] | ||