Information on Result #678894
Linear OA(4226, 16400, F4, 43) (dual of [16400, 16174, 44]-code), using construction X applied to C([0,21]) ⊂ C([0,20]) based on
- linear OA(4225, 16385, F4, 43) (dual of [16385, 16160, 44]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 414−1, defining interval I = [0,21], and minimum distance d ≥ |{−21,−20,…,21}|+1 = 44 (BCH-bound) [i]
- linear OA(4211, 16385, F4, 41) (dual of [16385, 16174, 42]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 414−1, defining interval I = [0,20], and minimum distance d ≥ |{−20,−19,…,20}|+1 = 42 (BCH-bound) [i]
- linear OA(41, 15, F4, 1) (dual of [15, 14, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(41, s, F4, 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 OA(4227, 16401, F4, 43) (dual of [16401, 16174, 44]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(4228, 16402, F4, 43) (dual of [16402, 16174, 44]-code) | [i] | ||
| 3 | Linear OOA(4226, 10801, F4, 2, 43) (dual of [(10801, 2), 21376, 44]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(4226, 10801, F4, 3, 43) (dual of [(10801, 3), 32177, 44]-NRT-code) | [i] | ||
| 5 | Digital (183, 226, 10801)-net over F4 | [i] | ||
| 6 | Linear OOA(4226, 8200, F4, 2, 43) (dual of [(8200, 2), 16174, 44]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(4226, 5466, F4, 3, 43) (dual of [(5466, 3), 16172, 44]-NRT-code) | [i] | ||