Information on Result #2235126
Linear OA(3221, 3285, F3, 42) (dual of [3285, 3064, 43]-code), using 1 times truncation based on linear OA(3222, 3286, F3, 43) (dual of [3286, 3064, 44]-code), using
- construction X applied to Ce(42) ⊂ Ce(40) [i] based on
- linear OA(3221, 3281, F3, 43) (dual of [3281, 3060, 44]-code), using an extension Ce(42) of the narrow-sense BCH-code C(I) with length 3280 | 38−1, defining interval I = [1,42], and designed minimum distance d ≥ |I|+1 = 43 [i]
- linear OA(3217, 3281, F3, 41) (dual of [3281, 3064, 42]-code), using an extension Ce(40) of the narrow-sense BCH-code C(I) with length 3280 | 38−1, defining interval I = [1,40], and designed minimum distance d ≥ |I|+1 = 41 [i]
- linear OA(31, 5, F3, 1) (dual of [5, 4, 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(3221, 3281, F3, 2, 42) (dual of [(3281, 2), 6341, 43]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3221, 3281, F3, 3, 42) (dual of [(3281, 3), 9622, 43]-NRT-code) | [i] | ||
| 3 | Linear OOA(3221, 3281, F3, 4, 42) (dual of [(3281, 4), 12903, 43]-NRT-code) | [i] | ||
| 4 | Linear OOA(3221, 3281, F3, 5, 42) (dual of [(3281, 5), 16184, 43]-NRT-code) | [i] | ||
| 5 | Digital (179, 221, 3281)-net over F3 | [i] | ||
| 6 | Linear OA(3223, 3306, F3, 42) (dual of [3306, 3083, 43]-code) | [i] | Varšamov–Edel Lengthening | |
| 7 | Linear OOA(3221, 1642, F3, 2, 42) (dual of [(1642, 2), 3063, 43]-NRT-code) | [i] | OOA Folding | |
| 8 | Linear OOA(3221, 1095, F3, 3, 42) (dual of [(1095, 3), 3064, 43]-NRT-code) | [i] | ||
| 9 | Linear OOA(3221, 821, F3, 4, 42) (dual of [(821, 4), 3063, 43]-NRT-code) | [i] | ||
| 10 | Linear OOA(3221, 657, F3, 5, 42) (dual of [(657, 5), 3064, 43]-NRT-code) | [i] | ||