Information on Result #2271646
Linear OA(4102, 16402, F4, 19) (dual of [16402, 16300, 20]-code), using 2 times code embedding in larger space based on linear OA(4100, 16400, F4, 19) (dual of [16400, 16300, 20]-code), using
- construction X applied to C([0,9]) ⊂ C([0,8]) [i] based on
- linear OA(499, 16385, F4, 19) (dual of [16385, 16286, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 414−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(485, 16385, F4, 17) (dual of [16385, 16300, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 414−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (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 OOA(4102, 9019, F4, 2, 19) (dual of [(9019, 2), 17936, 20]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4102, 9019, F4, 3, 19) (dual of [(9019, 3), 26955, 20]-NRT-code) | [i] | ||
| 3 | Digital (83, 102, 9019)-net over F4 | [i] | ||