Information on Result #2676994
Linear OOA(3136, 177152, F3, 3, 17) (dual of [(177152, 3), 531320, 18]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(3133, 177151, F3, 3, 17) (dual of [(177151, 3), 531320, 18]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3133, 531453, F3, 17) (dual of [531453, 531320, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(15) [i] based on
- linear OA(3133, 531441, F3, 17) (dual of [531441, 531308, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- 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(30, 12, F3, 0) (dual of [12, 12, 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(3136, 177152, F3, 4, 17) (dual of [(177152, 4), 708472, 18]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3136, 177152, F3, 5, 17) (dual of [(177152, 5), 885624, 18]-NRT-code) | [i] | ||
| 3 | Digital (119, 136, 177152)-net over F3 | [i] | ||