Information on Result #814316
Linear OOA(3172, 29550, F3, 2, 25) (dual of [(29550, 2), 58928, 26]-NRT-code), using OOA 2-folding based on linear OA(3172, 59100, F3, 25) (dual of [59100, 58928, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(3172, 59101, F3, 25) (dual of [59101, 58929, 26]-code), using
- construction X applied to C([0,12]) ⊂ C([0,9]) [i] based on
- linear OA(3161, 59050, F3, 25) (dual of [59050, 58889, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 59050 | 320−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- 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(311, 51, F3, 5) (dual of [51, 40, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(311, 85, F3, 5) (dual of [85, 74, 6]-code), using
- construction X applied to C([0,12]) ⊂ C([0,9]) [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(3172, 29550, F3, 2, 24) (dual of [(29550, 2), 58928, 25]-NRT-code) | [i] | Strength Reduction for OOAs | |
| 2 | Linear OOA(3172, 21991, F3, 3, 25) (dual of [(21991, 3), 65801, 26]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(3172, 21991, F3, 4, 25) (dual of [(21991, 4), 87792, 26]-NRT-code) | [i] | ||
| 4 | Linear OOA(3172, 21991, F3, 5, 25) (dual of [(21991, 5), 109783, 26]-NRT-code) | [i] | ||
| 5 | Digital (147, 172, 21991)-net over F3 | [i] | ||