Information on Result #2486837
Linear OOA(3164, 29536, F3, 2, 24) (dual of [(29536, 2), 58908, 25]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(3162, 29535, F3, 2, 24) (dual of [(29535, 2), 58908, 25]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3162, 59070, F3, 24) (dual of [59070, 58908, 25]-code), using
- construction X applied to Ce(24) ⊂ Ce(21) [i] based on
- linear OA(3161, 59049, F3, 25) (dual of [59049, 58888, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(3141, 59049, F3, 22) (dual of [59049, 58908, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(31, 21, F3, 1) (dual of [21, 20, 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
- construction X applied to Ce(24) ⊂ Ce(21) [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(3164, 20782, F3, 3, 24) (dual of [(20782, 3), 62182, 25]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3164, 20782, F3, 4, 24) (dual of [(20782, 4), 82964, 25]-NRT-code) | [i] | ||
| 3 | Linear OOA(3164, 20782, F3, 5, 24) (dual of [(20782, 5), 103746, 25]-NRT-code) | [i] | ||
| 4 | Digital (140, 164, 20782)-net over F3 | [i] | ||