Information on Result #813783
Linear OOA(3114, 3289, F3, 2, 21) (dual of [(3289, 2), 6464, 22]-NRT-code), using OOA 2-folding based on linear OA(3114, 6578, F3, 21) (dual of [6578, 6464, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(3114, 6579, F3, 21) (dual of [6579, 6465, 22]-code), using
- construction X applied to C([0,10]) ⊂ C([0,9]) [i] based on
- linear OA(3113, 6562, F3, 21) (dual of [6562, 6449, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 316−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(397, 6562, F3, 19) (dual of [6562, 6465, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 316−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(31, 17, F3, 1) (dual of [17, 16, 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 C([0,10]) ⊂ 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(3114, 3289, F3, 3, 21) (dual of [(3289, 3), 9753, 22]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3114, 3289, F3, 4, 21) (dual of [(3289, 4), 13042, 22]-NRT-code) | [i] | ||
| 3 | Linear OOA(3114, 3289, F3, 5, 21) (dual of [(3289, 5), 16331, 22]-NRT-code) | [i] | ||
| 4 | Digital (93, 114, 3289)-net over F3 | [i] | ||