Information on Result #952752
Linear OOA(3166, 531461, F3, 3, 18) (dual of [(531461, 3), 1594217, 19]-NRT-code), using OOA 3-folding based on linear OA(3166, 1594383, F3, 18) (dual of [1594383, 1594217, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(3166, 1594385, F3, 18) (dual of [1594385, 1594219, 19]-code), using
- construction X applied to C([0,9]) ⊂ C([0,6]) [i] based on
- linear OA(3157, 1594324, F3, 19) (dual of [1594324, 1594167, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 1594324 | 326−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(3105, 1594324, F3, 13) (dual of [1594324, 1594219, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 1594324 | 326−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(39, 61, F3, 4) (dual of [61, 52, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(39, 80, F3, 4) (dual of [80, 71, 5]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 80 = 34−1, defining interval I = [0,2], and designed minimum distance d ≥ |I|+1 = 5 [i]
- discarding factors / shortening the dual code based on linear OA(39, 80, F3, 4) (dual of [80, 71, 5]-code), using
- 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(3166, 531461, F3, 4, 18) (dual of [(531461, 4), 2125678, 19]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3166, 531461, F3, 5, 18) (dual of [(531461, 5), 2657139, 19]-NRT-code) | [i] | ||
| 3 | Digital (148, 166, 531461)-net over F3 | [i] | ||