Information on Result #737518
Linear OA(578, 78160, F5, 13) (dual of [78160, 78082, 14]-code), using construction X applied to Ce(12) ⊂ Ce(7) based on
- linear OA(571, 78125, F5, 13) (dual of [78125, 78054, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(543, 78125, F5, 8) (dual of [78125, 78082, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(57, 35, F5, 4) (dual of [35, 28, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(57, 44, F5, 4) (dual of [44, 37, 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 OOA(578, 78160, F5, 2, 13) (dual of [(78160, 2), 156242, 14]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(578, 78160, F5, 3, 13) (dual of [(78160, 3), 234402, 14]-NRT-code) | [i] | ||
| 3 | Digital (65, 78, 78160)-net over F5 | [i] | ||
| 4 | Linear OA(579, 78162, F5, 13) (dual of [78162, 78083, 14]-code) | [i] | Construction X with Varšamov Bound | |
| 5 | Linear OOA(578, 39080, F5, 2, 13) (dual of [(39080, 2), 78082, 14]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(578, 26053, F5, 3, 13) (dual of [(26053, 3), 78081, 14]-NRT-code) | [i] | ||
| 7 | Linear OOA(578, 13026, F5, 13, 13) (dual of [(13026, 13), 169260, 14]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |