Information on Result #2678655
Linear OOA(3224, 19687, F3, 3, 34) (dual of [(19687, 3), 58837, 35]-NRT-code), using 31 times duplication based on linear OOA(3223, 19687, F3, 3, 34) (dual of [(19687, 3), 58838, 35]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3223, 59061, F3, 34) (dual of [59061, 58838, 35]-code), using
- 1 times code embedding in larger space [i] based on linear OA(3222, 59060, F3, 34) (dual of [59060, 58838, 35]-code), using
- construction X applied to Ce(33) ⊂ Ce(31) [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(3211, 59049, F3, 32) (dual of [59049, 58838, 33]-code), using an extension Ce(31) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,31], and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(31, 11, F3, 1) (dual of [11, 10, 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(33) ⊂ Ce(31) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(3222, 59060, F3, 34) (dual of [59060, 58838, 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(3224, 19675, F3, 4, 34) (dual of [(19675, 4), 78476, 35]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3224, 19675, F3, 5, 34) (dual of [(19675, 5), 98151, 35]-NRT-code) | [i] | ||
| 3 | Digital (190, 224, 19675)-net over F3 | [i] | ||