Information on Result #682974
Linear OA(562, 3131, F5, 16) (dual of [3131, 3069, 17]-code), using construction X applied to Ce(15) ⊂ Ce(13) based on
- linear OA(561, 3125, F5, 16) (dual of [3125, 3064, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(556, 3125, F5, 14) (dual of [3125, 3069, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(51, 6, F5, 1) (dual of [6, 5, 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(561, 3130, F5, 15) (dual of [3130, 3069, 16]-code) | [i] | Truncation | |
| 2 | Linear OOA(562, 1669, F5, 2, 16) (dual of [(1669, 2), 3276, 17]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(562, 1669, F5, 3, 16) (dual of [(1669, 3), 4945, 17]-NRT-code) | [i] | ||
| 4 | Digital (46, 62, 1669)-net over F5 | [i] | ||
| 5 | Linear OOA(562, 1565, F5, 2, 16) (dual of [(1565, 2), 3068, 17]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(562, 1043, F5, 3, 16) (dual of [(1043, 3), 3067, 17]-NRT-code) | [i] | ||
| 7 | Linear OOA(562, 391, F5, 16, 16) (dual of [(391, 16), 6194, 17]-NRT-code) | [i] | OA Folding and Stacking | |