Information on Result #679392
Linear OA(4230, 4110, F4, 51) (dual of [4110, 3880, 52]-code), using construction X applied to C([0,25]) ⊂ C([0,24]) based on
- linear OA(4229, 4097, F4, 51) (dual of [4097, 3868, 52]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 412−1, defining interval I = [0,25], and minimum distance d ≥ |{−25,−24,…,25}|+1 = 52 (BCH-bound) [i]
- linear OA(4217, 4097, F4, 49) (dual of [4097, 3880, 50]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 412−1, defining interval I = [0,24], and minimum distance d ≥ |{−24,−23,…,24}|+1 = 50 (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(4231, 4111, F4, 51) (dual of [4111, 3880, 52]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(4232, 4112, F4, 51) (dual of [4112, 3880, 52]-code) | [i] | ||
| 3 | Linear OOA(4230, 4110, F4, 2, 51) (dual of [(4110, 2), 7990, 52]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(4230, 4110, F4, 3, 51) (dual of [(4110, 3), 12100, 52]-NRT-code) | [i] | ||
| 5 | Digital (179, 230, 4110)-net over F4 | [i] | ||
| 6 | Linear OA(4231, 4119, F4, 51) (dual of [4119, 3888, 52]-code) | [i] | Varšamov–Edel Lengthening | |
| 7 | Linear OA(4232, 4145, F4, 51) (dual of [4145, 3913, 52]-code) | [i] | ||
| 8 | Linear OA(4233, 4206, F4, 51) (dual of [4206, 3973, 52]-code) | [i] | ||
| 9 | Linear OA(4231, 4112, F4, 51) (dual of [4112, 3881, 52]-code) | [i] | Construction X with Varšamov Bound | |
| 10 | Linear OA(4232, 4114, F4, 51) (dual of [4114, 3882, 52]-code) | [i] | ||
| 11 | Linear OOA(4230, 2055, F4, 2, 51) (dual of [(2055, 2), 3880, 52]-NRT-code) | [i] | OOA Folding | |
| 12 | Linear OOA(4230, 1370, F4, 3, 51) (dual of [(1370, 3), 3880, 52]-NRT-code) | [i] | ||