Information on Result #731842
Linear OA(333, 59063, F3, 5) (dual of [59063, 59030, 6]-code), using (u, u+v)-construction based on
- linear OA(32, 4, F3, 2) (dual of [4, 2, 3]-code or 4-arc in PG(1,3)), using
- extended Reed–Solomon code RSe(2,3) [i]
- Hamming code H(2,3) [i]
- Simplex code S(2,3) [i]
- the Tetracode [i]
- linear OA(331, 59059, F3, 5) (dual of [59059, 59028, 6]-code), using
- construction X applied to Ce(4) ⊂ Ce(3) [i] based on
- linear OA(331, 59049, F3, 5) (dual of [59049, 59018, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(321, 59049, F3, 4) (dual of [59049, 59028, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(30, 10, F3, 0) (dual of [10, 10, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(30, s, F3, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(4) ⊂ Ce(3) [i] based on
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(333, 59063, F3, 2, 5) (dual of [(59063, 2), 118093, 6]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(333, 59063, F3, 3, 5) (dual of [(59063, 3), 177156, 6]-NRT-code) | [i] | ||
| 3 | Linear OOA(333, 59063, F3, 4, 5) (dual of [(59063, 4), 236219, 6]-NRT-code) | [i] | ||
| 4 | Linear OOA(333, 29531, F3, 2, 5) (dual of [(29531, 2), 59029, 6]-NRT-code) | [i] | OOA Folding | |