Information on Result #1782255
Digital (195, 228, 131096)-net over F4, using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(4228, 131096, F4, 2, 33) (dual of [(131096, 2), 261964, 34]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4228, 262192, F4, 33) (dual of [262192, 261964, 34]-code), using
- 1 times code embedding in larger space [i] based on linear OA(4227, 262191, F4, 33) (dual of [262191, 261964, 34]-code), using
- construction X applied to C([0,16]) ⊂ C([0,13]) [i] based on
- linear OA(4217, 262145, F4, 33) (dual of [262145, 261928, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 418−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
- linear OA(4181, 262145, F4, 27) (dual of [262145, 261964, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 418−1, defining interval I = [0,13], and minimum distance d ≥ |{−13,−12,…,13}|+1 = 28 (BCH-bound) [i]
- linear OA(410, 46, F4, 5) (dual of [46, 36, 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
- construction X applied to C([0,16]) ⊂ C([0,13]) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(4227, 262191, F4, 33) (dual of [262191, 261964, 34]-code), using
Mode: Linear.
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m and t, t and s.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Digital (196, 229, 131096)-net over F4 | [i] | Net Duplication | |