Information on Result #678077
Linear OA(4225, 1048621, F4, 28) (dual of [1048621, 1048396, 29]-code), using construction X applied to C([0,14]) ⊂ C([0,12]) based on
- linear OA(4221, 1048577, F4, 29) (dual of [1048577, 1048356, 30]-code), using the expurgated narrow-sense BCH-code C(I) with length 1048577 | 420−1, defining interval I = [0,14], and minimum distance d ≥ |{−14,−13,…,14}|+1 = 30 (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(44, 44, F4, 2) (dual of [44, 40, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(44, 85, F4, 2) (dual of [85, 81, 3]-code), using
- Hamming code H(4,4) [i]
- discarding factors / shortening the dual code based on linear OA(44, 85, F4, 2) (dual of [85, 81, 3]-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(4225, 540921, F4, 2, 28) (dual of [(540921, 2), 1081617, 29]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4225, 540921, F4, 3, 28) (dual of [(540921, 3), 1622538, 29]-NRT-code) | [i] | ||
| 3 | Digital (197, 225, 540921)-net over F4 | [i] | ||