Information on Result #952548
Linear OOA(3103, 19687, F3, 3, 16) (dual of [(19687, 3), 58958, 17]-NRT-code), using OOA 3-folding based on linear OA(3103, 59061, F3, 16) (dual of [59061, 58958, 17]-code), using
- 1 times code embedding in larger space [i] based on linear OA(3102, 59060, F3, 16) (dual of [59060, 58958, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(13) [i] based on
- linear OA(3101, 59049, F3, 16) (dual of [59049, 58948, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(391, 59049, F3, 14) (dual of [59049, 58958, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [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(15) ⊂ Ce(13) [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(3104, 19687, F3, 3, 16) (dual of [(19687, 3), 58957, 17]-NRT-code) | [i] | OOA Duplication | |
| 2 | Linear OOA(3103, 19687, F3, 4, 16) (dual of [(19687, 4), 78645, 17]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(3103, 19687, F3, 5, 16) (dual of [(19687, 5), 98332, 17]-NRT-code) | [i] | ||
| 4 | Digital (87, 103, 19687)-net over F3 | [i] | ||