Information on Result #2677165
Linear OOA(3135, 59053, F3, 3, 19) (dual of [(59053, 3), 177024, 20]-NRT-code), using 31 times duplication based on linear OOA(3134, 59053, F3, 3, 19) (dual of [(59053, 3), 177025, 20]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3134, 177159, F3, 19) (dual of [177159, 177025, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(16) [i] based on
- linear OA(3133, 177147, F3, 19) (dual of [177147, 177014, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- 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(31, 12, F3, 1) (dual of [12, 11, 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(18) ⊂ Ce(16) [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(3135, 50732, F3, 4, 19) (dual of [(50732, 4), 202793, 20]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3135, 50732, F3, 5, 19) (dual of [(50732, 5), 253525, 20]-NRT-code) | [i] | ||
| 3 | Digital (116, 135, 50732)-net over F3 | [i] | ||