Information on Result #682229
Linear OA(598, 390643, F5, 15) (dual of [390643, 390545, 16]-code), using construction X applied to C([0,7]) ⊂ C([0,6]) based on
- linear OA(597, 390626, F5, 15) (dual of [390626, 390529, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 390626 | 516−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- linear OA(581, 390626, F5, 13) (dual of [390626, 390545, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 390626 | 516−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(51, 17, F5, 1) (dual of [17, 16, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(51, s, F5, 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(598, 232660, F5, 2, 15) (dual of [(232660, 2), 465222, 16]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(598, 232660, F5, 3, 15) (dual of [(232660, 3), 697882, 16]-NRT-code) | [i] | ||
| 3 | Digital (83, 98, 232660)-net over F5 | [i] | ||
| 4 | Linear OOA(598, 130214, F5, 3, 15) (dual of [(130214, 3), 390544, 16]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(598, 55806, F5, 15, 15) (dual of [(55806, 15), 836992, 16]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |