Information on Result #2265586
Linear OA(3102, 2205, F3, 21) (dual of [2205, 2103, 22]-code), using 2 times code embedding in larger space based on linear OA(3100, 2203, F3, 21) (dual of [2203, 2103, 22]-code), using
- construction X applied to C([0,10]) ⊂ C([0,9]) [i] based on
- linear OA(399, 2188, F3, 21) (dual of [2188, 2089, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 2188 | 314−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(385, 2188, F3, 19) (dual of [2188, 2103, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 2188 | 314−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(31, 15, F3, 1) (dual of [15, 14, 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
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(3102, 1345, F3, 2, 21) (dual of [(1345, 2), 2588, 22]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3102, 1345, F3, 3, 21) (dual of [(1345, 3), 3933, 22]-NRT-code) | [i] | ||
| 3 | Linear OOA(3102, 1345, F3, 4, 21) (dual of [(1345, 4), 5278, 22]-NRT-code) | [i] | ||
| 4 | Linear OOA(3102, 1345, F3, 5, 21) (dual of [(1345, 5), 6623, 22]-NRT-code) | [i] | ||
| 5 | Digital (81, 102, 1345)-net over F3 | [i] | ||
| 6 | Linear OOA(3102, 735, F3, 3, 21) (dual of [(735, 3), 2103, 22]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(3102, 441, F3, 5, 21) (dual of [(441, 5), 2103, 22]-NRT-code) | [i] | ||