Information on Result #2487398
Linear OOA(3204, 29536, F3, 2, 30) (dual of [(29536, 2), 58868, 31]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(3202, 29535, F3, 2, 30) (dual of [(29535, 2), 58868, 31]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3202, 59070, F3, 30) (dual of [59070, 58868, 31]-code), using
- construction X applied to Ce(30) ⊂ Ce(27) [i] based on
- linear OA(3201, 59049, F3, 31) (dual of [59049, 58848, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(3181, 59049, F3, 28) (dual of [59049, 58868, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [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(30) ⊂ Ce(27) [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(3204, 20249, F3, 3, 30) (dual of [(20249, 3), 60543, 31]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3204, 20249, F3, 4, 30) (dual of [(20249, 4), 80792, 31]-NRT-code) | [i] | ||
| 3 | Linear OOA(3204, 20249, F3, 5, 30) (dual of [(20249, 5), 101041, 31]-NRT-code) | [i] | ||
| 4 | Digital (174, 204, 20249)-net over F3 | [i] | ||