Information on Result #682482
Linear OA(5107, 78148, F5, 18) (dual of [78148, 78041, 19]-code), using construction X4 applied to Ce(18) ⊂ Ce(15) based on
- linear OA(5106, 78125, F5, 19) (dual of [78125, 78019, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [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(522, 23, F5, 22) (dual of [23, 1, 23]-code or 23-arc in PG(21,5)), using
- dual of repetition code with length 23 [i]
- linear OA(51, 23, F5, 1) (dual of [23, 22, 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(5107, 72626, F5, 2, 18) (dual of [(72626, 2), 145145, 19]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(5107, 72626, F5, 3, 18) (dual of [(72626, 3), 217771, 19]-NRT-code) | [i] | ||
| 3 | Digital (89, 107, 72626)-net over F5 | [i] | ||