Information on Result #952560
Linear OOA(3124, 177152, F3, 3, 16) (dual of [(177152, 3), 531332, 17]-NRT-code), using OOA 3-folding based on linear OA(3124, 531456, F3, 16) (dual of [531456, 531332, 17]-code), using
- 2 times code embedding in larger space [i] based on linear OA(3122, 531454, F3, 16) (dual of [531454, 531332, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(13) [i] based on
- linear OA(3121, 531441, F3, 16) (dual of [531441, 531320, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(3109, 531441, F3, 14) (dual of [531441, 531332, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(31, 13, F3, 1) (dual of [13, 12, 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(3124, 171110, F3, 4, 16) (dual of [(171110, 4), 684316, 17]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3124, 171110, F3, 5, 16) (dual of [(171110, 5), 855426, 17]-NRT-code) | [i] | ||
| 3 | Digital (108, 124, 171110)-net over F3 | [i] | ||