Information on Result #683006
Linear OA(564, 3138, F5, 16) (dual of [3138, 3074, 17]-code), using construction X applied to Ce(15) ⊂ Ce(12) 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(551, 3125, F5, 13) (dual of [3125, 3074, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(53, 13, F5, 2) (dual of [13, 10, 3]-code), using
- discarding factors / shortening the dual code based on 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]
- discarding factors / shortening the dual code based on linear OA(53, 24, F5, 2) (dual of [24, 21, 3]-code), 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(564, 2103, F5, 2, 16) (dual of [(2103, 2), 4142, 17]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(564, 2103, F5, 3, 16) (dual of [(2103, 3), 6245, 17]-NRT-code) | [i] | ||
| 3 | Digital (48, 64, 2103)-net over F5 | [i] | ||
| 4 | Linear OOA(564, 1569, F5, 2, 16) (dual of [(1569, 2), 3074, 17]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(564, 1046, F5, 3, 16) (dual of [(1046, 3), 3074, 17]-NRT-code) | [i] | ||
| 6 | Linear OOA(564, 392, F5, 16, 16) (dual of [(392, 16), 6208, 17]-NRT-code) | [i] | OA Folding and Stacking | |