Information on Result #674803
Linear OA(3142, 59072, F3, 21) (dual of [59072, 58930, 22]-code), using construction X4 applied to C([0,10]) ⊂ C([0,9]) based on
- linear OA(3141, 59050, F3, 21) (dual of [59050, 58909, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 59050 | 320−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(3121, 59050, F3, 19) (dual of [59050, 58929, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 59050 | 320−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(321, 22, F3, 21) (dual of [22, 1, 22]-code or 22-arc in PG(20,3)), using
- dual of repetition code with length 22 [i]
- linear OA(31, 22, F3, 1) (dual of [22, 21, 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, 59073, F3, 21) (dual of [59073, 58930, 22]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(3144, 59074, F3, 21) (dual of [59074, 58930, 22]-code) | [i] | ||
| 3 | Linear OA(3145, 59075, F3, 21) (dual of [59075, 58930, 22]-code) | [i] | ||
| 4 | Linear OOA(3142, 29536, F3, 2, 21) (dual of [(29536, 2), 58930, 22]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(3142, 14768, F3, 4, 21) (dual of [(14768, 4), 58930, 22]-NRT-code) | [i] | ||