Information on Result #736946
Linear OA(3215, 19744, F3, 34) (dual of [19744, 19529, 35]-code), using construction X applied to Ce(33) ⊂ Ce(25) based on
- linear OA(3199, 19683, F3, 34) (dual of [19683, 19484, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(3154, 19683, F3, 26) (dual of [19683, 19529, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(316, 61, F3, 7) (dual of [61, 45, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(316, 82, F3, 7) (dual of [82, 66, 8]-code), 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(3217, 19746, F3, 34) (dual of [19746, 19529, 35]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(3218, 19747, F3, 34) (dual of [19747, 19529, 35]-code) | [i] | ||
| 3 | Linear OA(3219, 19748, F3, 34) (dual of [19748, 19529, 35]-code) | [i] | ||
| 4 | Linear OA(3214, 19743, F3, 33) (dual of [19743, 19529, 34]-code) | [i] | Truncation | |
| 5 | Linear OOA(3215, 9891, F3, 2, 34) (dual of [(9891, 2), 19567, 35]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 6 | Linear OOA(3215, 9891, F3, 3, 34) (dual of [(9891, 3), 29458, 35]-NRT-code) | [i] | ||
| 7 | Linear OOA(3215, 9891, F3, 4, 34) (dual of [(9891, 4), 39349, 35]-NRT-code) | [i] | ||
| 8 | Linear OOA(3215, 9891, F3, 5, 34) (dual of [(9891, 5), 49240, 35]-NRT-code) | [i] | ||
| 9 | Digital (181, 215, 9891)-net over F3 | [i] | ||
| 10 | Linear OA(3219, 19749, F3, 34) (dual of [19749, 19530, 35]-code) | [i] | Construction X with Varšamov Bound | |
| 11 | Linear OOA(3215, 9872, F3, 2, 34) (dual of [(9872, 2), 19529, 35]-NRT-code) | [i] | OOA Folding | |
| 12 | Linear OOA(3215, 6581, F3, 3, 34) (dual of [(6581, 3), 19528, 35]-NRT-code) | [i] | ||
| 13 | Linear OOA(3215, 4936, F3, 4, 34) (dual of [(4936, 4), 19529, 35]-NRT-code) | [i] | ||
| 14 | Linear OOA(3215, 3948, F3, 5, 34) (dual of [(3948, 5), 19525, 35]-NRT-code) | [i] | ||