Information on Result #1301560
Linear OA(588, 78171, F5, 14) (dual of [78171, 78083, 15]-code), using construction X with Varšamov bound based on
- linear OA(587, 78169, F5, 14) (dual of [78169, 78082, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(7) [i] based on
- linear OA(578, 78125, F5, 14) (dual of [78125, 78047, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [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(59, 44, F5, 5) (dual of [44, 35, 6]-code), using
- construction X applied to Ce(13) ⊂ Ce(7) [i] based on
- linear OA(587, 78170, F5, 13) (dual of [78170, 78083, 14]-code), using Gilbert–Varšamov bound and bm = 587 > Vbs−1(k−1) = 1821 577160 700635 461618 895327 238024 428986 335790 612616 792869 [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(588, 78171, F5, 2, 14) (dual of [(78171, 2), 156254, 15]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(588, 78171, F5, 3, 14) (dual of [(78171, 3), 234425, 15]-NRT-code) | [i] | ||
| 3 | Digital (74, 88, 78171)-net over F5 | [i] | ||