Information on Result #2678470
Linear OOA(3234, 59053, F3, 3, 32) (dual of [(59053, 3), 176925, 33]-NRT-code), using 31 times duplication based on linear OOA(3233, 59053, F3, 3, 32) (dual of [(59053, 3), 176926, 33]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3233, 177159, F3, 32) (dual of [177159, 176926, 33]-code), using
- 1 times code embedding in larger space [i] based on linear OA(3232, 177158, F3, 32) (dual of [177158, 176926, 33]-code), using
- construction X applied to Ce(31) ⊂ Ce(30) [i] based on
- linear OA(3232, 177147, F3, 32) (dual of [177147, 176915, 33]-code), using an extension Ce(31) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,31], and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(3221, 177147, F3, 31) (dual of [177147, 176926, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [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(31) ⊂ Ce(30) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(3232, 177158, F3, 32) (dual of [177158, 176926, 33]-code), using
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(3234, 48751, F3, 4, 32) (dual of [(48751, 4), 194770, 33]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3234, 48751, F3, 5, 32) (dual of [(48751, 5), 243521, 33]-NRT-code) | [i] | ||
| 3 | Digital (202, 234, 48751)-net over F3 | [i] | ||