Information on Result #1301506
Linear OA(579, 78162, F5, 13) (dual of [78162, 78083, 14]-code), using construction X with Varšamov bound based on
- linear OA(578, 78160, F5, 13) (dual of [78160, 78082, 14]-code), using
- construction X applied to Ce(12) ⊂ Ce(7) [i] 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
- construction X applied to Ce(12) ⊂ Ce(7) [i] based on
- linear OA(578, 78161, F5, 12) (dual of [78161, 78083, 13]-code), using Gilbert–Varšamov bound and bm = 578 > Vbs−1(k−1) = 69830 299833 750382 725278 077292 090410 960130 413663 324865 [i]
- linear OA(50, 1, F5, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(50, s, F5, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
Mode: 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(579, 78162, F5, 2, 13) (dual of [(78162, 2), 156245, 14]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(579, 78162, F5, 3, 13) (dual of [(78162, 3), 234407, 14]-NRT-code) | [i] | ||
| 3 | Digital (66, 79, 78162)-net over F5 | [i] | ||