Information on Result #1301669
Linear OA(5104, 78175, F5, 17) (dual of [78175, 78071, 18]-code), using construction X with Varšamov bound based on
- linear OA(5101, 78169, F5, 17) (dual of [78169, 78068, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(10) [i] based on
- linear OA(592, 78125, F5, 17) (dual of [78125, 78033, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(557, 78125, F5, 11) (dual of [78125, 78068, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(59, 44, F5, 5) (dual of [44, 35, 6]-code), using
- construction X applied to Ce(16) ⊂ Ce(10) [i] based on
- linear OA(5101, 78172, F5, 16) (dual of [78172, 78071, 17]-code), using Gilbert–Varšamov bound and bm = 5101 > Vbs−1(k−1) = 20394 953891 574889 972015 583081 550216 877768 996882 849382 492448 088593 421981 [i]
- linear OA(50, 3, F5, 0) (dual of [3, 3, 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(5104, 78175, F5, 2, 17) (dual of [(78175, 2), 156246, 18]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(5104, 78175, F5, 3, 17) (dual of [(78175, 3), 234421, 18]-NRT-code) | [i] | ||
| 3 | Digital (87, 104, 78175)-net over F5 | [i] | ||
| 4 | Linear OOA(5104, 39087, F5, 2, 17) (dual of [(39087, 2), 78070, 18]-NRT-code) | [i] | OOA Folding | |