Information on Result #813461
Linear OOA(3129, 29545, F3, 2, 18) (dual of [(29545, 2), 58961, 19]-NRT-code), using OOA 2-folding based on linear OA(3129, 59090, F3, 18) (dual of [59090, 58961, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(3129, 59091, F3, 18) (dual of [59091, 58962, 19]-code), using
- construction X applied to C([0,9]) ⊂ C([0,6]) [i] based on
- linear OA(3121, 59050, F3, 19) (dual of [59050, 58929, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 59050 | 320−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(381, 59050, F3, 13) (dual of [59050, 58969, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 59050 | 320−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(38, 41, F3, 4) (dual of [41, 33, 5]-code), using
- the narrow-sense BCH-code C(I) with length 41 | 38−1, defining interval I = [1,1], and minimum distance d ≥ |{−3,−1,1,3}|+1 = 5 (BCH-bound) [i]
- construction X applied to C([0,9]) ⊂ C([0,6]) [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(3129, 29545, F3, 3, 18) (dual of [(29545, 3), 88506, 19]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3129, 29545, F3, 4, 18) (dual of [(29545, 4), 118051, 19]-NRT-code) | [i] | ||
| 3 | Linear OOA(3129, 29545, F3, 5, 18) (dual of [(29545, 5), 147596, 19]-NRT-code) | [i] | ||
| 4 | Digital (111, 129, 29545)-net over F3 | [i] | ||