Information on Result #2678265
Linear OOA(3224, 59057, F3, 3, 30) (dual of [(59057, 3), 176947, 31]-NRT-code), using 31 times duplication based on linear OOA(3223, 59057, F3, 3, 30) (dual of [(59057, 3), 176948, 31]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3223, 177171, F3, 30) (dual of [177171, 176948, 31]-code), using
- 1 times code embedding in larger space [i] based on linear OA(3222, 177170, F3, 30) (dual of [177170, 176948, 31]-code), using
- construction X applied to Ce(30) ⊂ Ce(27) [i] based on
- 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(3199, 177147, F3, 28) (dual of [177147, 176948, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(31, 23, F3, 1) (dual of [23, 22, 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(30) ⊂ Ce(27) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(3222, 177170, F3, 30) (dual of [177170, 176948, 31]-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(3224, 59057, F3, 4, 30) (dual of [(59057, 4), 236004, 31]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3224, 59057, F3, 5, 30) (dual of [(59057, 5), 295061, 31]-NRT-code) | [i] | ||
| 3 | Digital (194, 224, 59057)-net over F3 | [i] | ||