Information on Result #2208859
Linear OA(4259, 1048655, F4, 32) (dual of [1048655, 1048396, 33]-code), using strength reduction based on linear OA(4259, 1048655, F4, 33) (dual of [1048655, 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(418, 78, F4, 7) (dual of [78, 60, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(418, 85, F4, 7) (dual of [85, 67, 8]-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(4259, 604458, F4, 2, 32) (dual of [(604458, 2), 1208657, 33]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4259, 604458, F4, 3, 32) (dual of [(604458, 3), 1813115, 33]-NRT-code) | [i] | ||
| 3 | Digital (227, 259, 604458)-net over F4 | [i] | ||