Information on Result #952833
Linear OOA(3123, 19687, F3, 3, 19) (dual of [(19687, 3), 58938, 20]-NRT-code), using OOA 3-folding based on linear OA(3123, 59061, F3, 19) (dual of [59061, 58938, 20]-code), using
- 1 times code embedding in larger space [i] based on linear OA(3122, 59060, F3, 19) (dual of [59060, 58938, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(16) [i] based on
- linear OA(3121, 59049, F3, 19) (dual of [59049, 58928, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(3111, 59049, F3, 17) (dual of [59049, 58938, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [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(18) ⊂ Ce(16) [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(3124, 19687, F3, 3, 19) (dual of [(19687, 3), 58937, 20]-NRT-code) | [i] | OOA Duplication | |
| 2 | Linear OOA(3123, 19687, F3, 4, 19) (dual of [(19687, 4), 78625, 20]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(3123, 19687, F3, 5, 19) (dual of [(19687, 5), 98312, 20]-NRT-code) | [i] | ||
| 4 | Digital (104, 123, 19687)-net over F3 | [i] | ||