Information on Result #952641
Linear OOA(3123, 59053, F3, 3, 17) (dual of [(59053, 3), 177036, 18]-NRT-code), using OOA 3-folding based on linear OA(3123, 177159, F3, 17) (dual of [177159, 177036, 18]-code), using
- 1 times code embedding in larger space [i] based on linear OA(3122, 177158, F3, 17) (dual of [177158, 177036, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(15) [i] based on
- linear OA(3122, 177147, F3, 17) (dual of [177147, 177025, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(3111, 177147, F3, 16) (dual of [177147, 177036, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(30, 11, F3, 0) (dual of [11, 11, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(30, s, F3, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(16) ⊂ Ce(15) [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, 59053, F3, 3, 17) (dual of [(59053, 3), 177035, 18]-NRT-code) | [i] | OOA Duplication | |
| 2 | Linear OOA(3125, 59053, F3, 3, 17) (dual of [(59053, 3), 177034, 18]-NRT-code) | [i] | ||
| 3 | Linear OOA(3123, 59053, F3, 4, 17) (dual of [(59053, 4), 236089, 18]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(3123, 59053, F3, 5, 17) (dual of [(59053, 5), 295142, 18]-NRT-code) | [i] | ||
| 5 | Digital (106, 123, 59053)-net over F3 | [i] | ||