Information on Result #2487784
Linear OOA(3241, 29559, F3, 2, 34) (dual of [(29559, 2), 58877, 35]-NRT-code), using 31 times duplication based on linear OOA(3240, 29559, F3, 2, 34) (dual of [(29559, 2), 58878, 35]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(3238, 29558, F3, 2, 34) (dual of [(29558, 2), 58878, 35]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3238, 59116, F3, 34) (dual of [59116, 58878, 35]-code), using
- construction X applied to Ce(33) ⊂ Ce(25) [i] based on
- linear OA(3221, 59049, F3, 34) (dual of [59049, 58828, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(3171, 59049, F3, 26) (dual of [59049, 58878, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(317, 67, F3, 7) (dual of [67, 50, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(317, 80, F3, 7) (dual of [80, 63, 8]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 80 = 34−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 8 [i]
- discarding factors / shortening the dual code based on linear OA(317, 80, F3, 7) (dual of [80, 63, 8]-code), using
- construction X applied to Ce(33) ⊂ Ce(25) [i] based on
- OOA 2-folding [i] based on linear OA(3238, 59116, F3, 34) (dual of [59116, 58878, 35]-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 OOA(3241, 29559, F3, 3, 34) (dual of [(29559, 3), 88436, 35]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3241, 29559, F3, 4, 34) (dual of [(29559, 4), 117995, 35]-NRT-code) | [i] | ||
| 3 | Linear OOA(3241, 29559, F3, 5, 34) (dual of [(29559, 5), 147554, 35]-NRT-code) | [i] | ||
| 4 | Digital (207, 241, 29559)-net over F3 | [i] | ||