Information on Result #679410
Linear OA(4122, 4110, F4, 27) (dual of [4110, 3988, 28]-code), using construction X applied to C([0,13]) ⊂ C([0,12]) based on
- linear OA(4121, 4097, F4, 27) (dual of [4097, 3976, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 412−1, defining interval I = [0,13], and minimum distance d ≥ |{−13,−12,…,13}|+1 = 28 (BCH-bound) [i]
- linear OA(4109, 4097, F4, 25) (dual of [4097, 3988, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 412−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(41, 13, F4, 1) (dual of [13, 12, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(41, s, F4, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, 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 OA(4123, 4111, F4, 27) (dual of [4111, 3988, 28]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(4124, 4112, F4, 27) (dual of [4112, 3988, 28]-code) | [i] | ||
| 3 | Linear OOA(4122, 2763, F4, 2, 27) (dual of [(2763, 2), 5404, 28]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(4122, 2763, F4, 3, 27) (dual of [(2763, 3), 8167, 28]-NRT-code) | [i] | ||
| 5 | Digital (95, 122, 2763)-net over F4 | [i] | ||
| 6 | Linear OA(4127, 4125, F4, 27) (dual of [4125, 3998, 28]-code) | [i] | Varšamov–Edel Lengthening | |
| 7 | Linear OOA(4122, 2055, F4, 2, 27) (dual of [(2055, 2), 3988, 28]-NRT-code) | [i] | OOA Folding | |
| 8 | Linear OOA(4122, 1370, F4, 3, 27) (dual of [(1370, 3), 3988, 28]-NRT-code) | [i] | ||