Information on Result #683451
Linear OA(550, 630, F5, 16) (dual of [630, 580, 17]-code), using construction X applied to Ce(15) ⊂ Ce(13) based on
- linear OA(549, 625, F5, 16) (dual of [625, 576, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(545, 625, F5, 14) (dual of [625, 580, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(51, 5, F5, 1) (dual of [5, 4, 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(550, 414, F5, 2, 16) (dual of [(414, 2), 778, 17]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(550, 414, F5, 3, 16) (dual of [(414, 3), 1192, 17]-NRT-code) | [i] | ||
| 3 | Digital (34, 50, 414)-net over F5 | [i] | ||
| 4 | Linear OA(554, 647, F5, 16) (dual of [647, 593, 17]-code) | [i] | Varšamov–Edel Lengthening | |
| 5 | Linear OA(555, 665, F5, 16) (dual of [665, 610, 17]-code) | [i] | ||
| 6 | Linear OOA(550, 315, F5, 2, 16) (dual of [(315, 2), 580, 17]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(550, 210, F5, 3, 16) (dual of [(210, 3), 580, 17]-NRT-code) | [i] | ||