Information on Result #737561
Linear OA(567, 15655, F5, 13) (dual of [15655, 15588, 14]-code), using construction X applied to Ce(12) ⊂ Ce(7) based on
- linear OA(561, 15625, F5, 13) (dual of [15625, 15564, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(537, 15625, F5, 8) (dual of [15625, 15588, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(56, 30, F5, 4) (dual of [30, 24, 5]-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 OA(568, 15656, F5, 13) (dual of [15656, 15588, 14]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(567, 15655, F5, 2, 13) (dual of [(15655, 2), 31243, 14]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(567, 15655, F5, 3, 13) (dual of [(15655, 3), 46898, 14]-NRT-code) | [i] | ||
| 4 | Digital (54, 67, 15655)-net over F5 | [i] | ||
| 5 | Linear OA(568, 15657, F5, 13) (dual of [15657, 15589, 14]-code) | [i] | Construction X with Varšamov Bound | |
| 6 | Linear OA(569, 15659, F5, 13) (dual of [15659, 15590, 14]-code) | [i] | ||
| 7 | Linear OOA(567, 7827, F5, 2, 13) (dual of [(7827, 2), 15587, 14]-NRT-code) | [i] | OOA Folding | |
| 8 | Linear OOA(567, 5218, F5, 3, 13) (dual of [(5218, 3), 15587, 14]-NRT-code) | [i] | ||
| 9 | Linear OOA(567, 2609, F5, 13, 13) (dual of [(2609, 13), 33850, 14]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |