Information on Result #678577
Linear OA(4171, 65579, F4, 27) (dual of [65579, 65408, 28]-code), using construction X applied to C([0,13]) ⊂ C([0,10]) based on
- linear OA(4161, 65537, F4, 27) (dual of [65537, 65376, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 416−1, defining interval I = [0,13], and minimum distance d ≥ |{−13,−12,…,13}|+1 = 28 (BCH-bound) [i]
- linear OA(4129, 65537, F4, 21) (dual of [65537, 65408, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 416−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(410, 42, F4, 5) (dual of [42, 32, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(410, 63, F4, 5) (dual of [63, 53, 6]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,3], and designed minimum distance d ≥ |I|+1 = 6 [i]
- discarding factors / shortening the dual code based on linear OA(410, 63, F4, 5) (dual of [63, 53, 6]-code), 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(4171, 42103, F4, 2, 27) (dual of [(42103, 2), 84035, 28]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4171, 42103, F4, 3, 27) (dual of [(42103, 3), 126138, 28]-NRT-code) | [i] | ||
| 3 | Digital (144, 171, 42103)-net over F4 | [i] | ||