Information on Result #2273469
Linear OA(4259, 65603, F4, 41) (dual of [65603, 65344, 42]-code), using 2 times code embedding in larger space based on linear OA(4257, 65601, F4, 41) (dual of [65601, 65344, 42]-code), using
- construction X applied to C([0,20]) ⊂ C([0,16]) [i] based on
- linear OA(4241, 65537, F4, 41) (dual of [65537, 65296, 42]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 416−1, defining interval I = [0,20], and minimum distance d ≥ |{−20,−19,…,20}|+1 = 42 (BCH-bound) [i]
- linear OA(4193, 65537, F4, 33) (dual of [65537, 65344, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 416−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
- linear OA(416, 64, F4, 7) (dual of [64, 48, 8]-code), using
- an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
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(4259, 49304, F4, 2, 41) (dual of [(49304, 2), 98349, 42]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4259, 49304, F4, 3, 41) (dual of [(49304, 3), 147653, 42]-NRT-code) | [i] | ||
| 3 | Digital (218, 259, 49304)-net over F4 | [i] | ||