Information on Result #691877
Linear OA(1638, 4104, F16, 13) (dual of [4104, 4066, 14]-code), using construction X applied to C([0,6]) ⊂ C([0,5]) based on
- linear OA(1637, 4097, F16, 13) (dual of [4097, 4060, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 166−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(1631, 4097, F16, 11) (dual of [4097, 4066, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 166−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- linear OA(161, 7, F16, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(161, s, F16, 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 OOA(1638, 3669, F16, 2, 13) (dual of [(3669, 2), 7300, 14]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (25, 38, 3669)-net over F16 | [i] | ||
| 3 | Linear OOA(1638, 2052, F16, 2, 13) (dual of [(2052, 2), 4066, 14]-NRT-code) | [i] | OOA Folding | |