Information on Result #1785141
Digital (225, 258, 524327)-net over F4, using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(4258, 524327, F4, 2, 33) (dual of [(524327, 2), 1048396, 34]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(4256, 524326, F4, 2, 33) (dual of [(524326, 2), 1048396, 34]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4256, 1048652, F4, 33) (dual of [1048652, 1048396, 34]-code), using
- construction X applied to C([0,16]) ⊂ C([0,12]) [i] based on
- linear OA(4241, 1048577, F4, 33) (dual of [1048577, 1048336, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 1048577 | 420−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
- linear OA(4181, 1048577, F4, 25) (dual of [1048577, 1048396, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 1048577 | 420−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(415, 75, F4, 7) (dual of [75, 60, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(415, 85, F4, 7) (dual of [85, 70, 8]-code), using
- construction X applied to C([0,16]) ⊂ C([0,12]) [i] based on
- OOA 2-folding [i] based on linear OA(4256, 1048652, F4, 33) (dual of [1048652, 1048396, 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 (226, 259, 524327)-net over F4 | [i] | Net Duplication | |