Information on Result #2277327
Linear OA(5101, 78141, F5, 18) (dual of [78141, 78040, 19]-code), using 1 times code embedding in larger space based on linear OA(5100, 78140, F5, 18) (dual of [78140, 78040, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(15) [i] based on
- linear OA(599, 78125, F5, 18) (dual of [78125, 78026, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(585, 78125, F5, 16) (dual of [78125, 78040, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(51, 15, F5, 1) (dual of [15, 14, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(51, s, F5, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, 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(5101, 39712, F5, 2, 18) (dual of [(39712, 2), 79323, 19]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(5101, 39712, F5, 3, 18) (dual of [(39712, 3), 119035, 19]-NRT-code) | [i] | ||
| 3 | Digital (83, 101, 39712)-net over F5 | [i] | ||
| 4 | Linear OOA(5101, 26047, F5, 3, 18) (dual of [(26047, 3), 78040, 19]-NRT-code) | [i] | OOA Folding | |