Information on Result #678911
Linear OA(4128, 16400, F4, 23) (dual of [16400, 16272, 24]-code), using construction X applied to C([0,12]) ⊂ C([0,10]) based on
- linear OA(4127, 16385, F4, 25) (dual of [16385, 16258, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 414−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(4113, 16385, F4, 21) (dual of [16385, 16272, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 414−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (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(4128, 12643, F4, 2, 23) (dual of [(12643, 2), 25158, 24]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4128, 12643, F4, 3, 23) (dual of [(12643, 3), 37801, 24]-NRT-code) | [i] | ||
| 3 | Digital (105, 128, 12643)-net over F4 | [i] | ||