Information on Result #682577
Linear OA(5110, 15639, F5, 23) (dual of [15639, 15529, 24]-code), using construction X applied to C([0,11]) ⊂ C([0,10]) based on
- linear OA(5109, 15626, F5, 23) (dual of [15626, 15517, 24]-code), using the expurgated narrow-sense BCH-code C(I) with length 15626 | 512−1, defining interval I = [0,11], and minimum distance d ≥ |{−11,−10,…,11}|+1 = 24 (BCH-bound) [i]
- linear OA(597, 15626, F5, 21) (dual of [15626, 15529, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 15626 | 512−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(51, 13, F5, 1) (dual of [13, 12, 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 OA(5111, 15640, F5, 23) (dual of [15640, 15529, 24]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(5112, 15641, F5, 23) (dual of [15641, 15529, 24]-code) | [i] | ||
| 3 | Linear OOA(5110, 9199, F5, 2, 23) (dual of [(9199, 2), 18288, 24]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(5110, 9199, F5, 3, 23) (dual of [(9199, 3), 27487, 24]-NRT-code) | [i] | ||
| 5 | Digital (87, 110, 9199)-net over F5 | [i] | ||
| 6 | Linear OOA(5110, 7819, F5, 2, 23) (dual of [(7819, 2), 15528, 24]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(5110, 5213, F5, 3, 23) (dual of [(5213, 3), 15529, 24]-NRT-code) | [i] | ||
| 8 | Linear OOA(5110, 1421, F5, 23, 23) (dual of [(1421, 23), 32573, 24]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |