Information on Result #2277357
Linear OA(5110, 78150, F5, 19) (dual of [78150, 78040, 20]-code), using 1 times code embedding in larger space based on linear OA(5109, 78149, F5, 19) (dual of [78149, 78040, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(15) [i] 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(53, 24, F5, 2) (dual of [24, 21, 3]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 24 = 52−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 3 [i]
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(5110, 54378, F5, 2, 19) (dual of [(54378, 2), 108646, 20]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(5110, 54378, F5, 3, 19) (dual of [(54378, 3), 163024, 20]-NRT-code) | [i] | ||
| 3 | Digital (91, 110, 54378)-net over F5 | [i] | ||
| 4 | Linear OOA(5110, 39075, F5, 2, 19) (dual of [(39075, 2), 78040, 20]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(5110, 26050, F5, 3, 19) (dual of [(26050, 3), 78040, 20]-NRT-code) | [i] | ||