Information on Result #679469
Linear OA(4155, 4131, F4, 33) (dual of [4131, 3976, 34]-code), using construction X applied to C([0,16]) ⊂ C([0,13]) based on
- linear OA(4145, 4097, F4, 33) (dual of [4097, 3952, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 412−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
- 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(410, 34, F4, 5) (dual of [34, 24, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(410, 63, F4, 5) (dual of [63, 53, 6]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,3], and designed minimum distance d ≥ |I|+1 = 6 [i]
- discarding factors / shortening the dual code based on linear OA(410, 63, F4, 5) (dual of [63, 53, 6]-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(4155, 4029, F4, 2, 33) (dual of [(4029, 2), 7903, 34]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4155, 4029, F4, 3, 33) (dual of [(4029, 3), 11932, 34]-NRT-code) | [i] | ||
| 3 | Digital (122, 155, 4029)-net over F4 | [i] | ||
| 4 | Linear OOA(4155, 1377, F4, 3, 33) (dual of [(1377, 3), 3976, 34]-NRT-code) | [i] | OOA Folding | |