Information on Result #952569
Linear OOA(3139, 531454, F3, 3, 16) (dual of [(531454, 3), 1594223, 17]-NRT-code), using OOA 3-folding based on linear OA(3139, 1594362, F3, 16) (dual of [1594362, 1594223, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(3139, 1594364, F3, 16) (dual of [1594364, 1594225, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(10) [i] based on
- linear OA(3131, 1594323, F3, 16) (dual of [1594323, 1594192, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(392, 1594323, F3, 11) (dual of [1594323, 1594231, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(38, 41, F3, 4) (dual of [41, 33, 5]-code), using
- the narrow-sense BCH-code C(I) with length 41 | 38−1, defining interval I = [1,1], and minimum distance d ≥ |{−3,−1,1,3}|+1 = 5 (BCH-bound) [i]
- construction X applied to Ce(15) ⊂ Ce(10) [i] based on
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(3139, 531454, F3, 4, 16) (dual of [(531454, 4), 2125677, 17]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3139, 531454, F3, 5, 16) (dual of [(531454, 5), 2657131, 17]-NRT-code) | [i] | ||
| 3 | Digital (123, 139, 531454)-net over F3 | [i] | ||