Information on Result #682435
Linear OA(586, 78133, F5, 16) (dual of [78133, 78047, 17]-code), using construction X applied to Ce(15) ⊂ Ce(13) based on
- 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(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(51, 8, F5, 1) (dual of [8, 7, 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 OA(585, 78132, F5, 15) (dual of [78132, 78047, 16]-code) | [i] | Truncation | |
| 2 | Linear OOA(586, 39066, F5, 2, 16) (dual of [(39066, 2), 78046, 17]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(586, 26044, F5, 3, 16) (dual of [(26044, 3), 78046, 17]-NRT-code) | [i] | ||
| 4 | Linear OOA(586, 9766, F5, 16, 16) (dual of [(9766, 16), 156170, 17]-NRT-code) | [i] | OA Folding and Stacking | |