Information on Result #952568
Linear OOA(3135, 531451, F3, 3, 16) (dual of [(531451, 3), 1594218, 17]-NRT-code), using OOA 3-folding based on linear OA(3135, 1594353, F3, 16) (dual of [1594353, 1594218, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(12) [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(3105, 1594323, F3, 13) (dual of [1594323, 1594218, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(34, 30, F3, 2) (dual of [30, 26, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(34, 40, F3, 2) (dual of [40, 36, 3]-code), using
- Hamming code H(4,3) [i]
- discarding factors / shortening the dual code based on linear OA(34, 40, F3, 2) (dual of [40, 36, 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(3135, 531451, F3, 3, 15) (dual of [(531451, 3), 1594218, 16]-NRT-code) | [i] | Strength Reduction for OOAs | |
| 2 | Linear OOA(3138, 531452, F3, 3, 16) (dual of [(531452, 3), 1594218, 17]-NRT-code) | [i] | NRT-Code Embedding in Larger Space | |
| 3 | Linear OOA(3136, 531451, F3, 3, 16) (dual of [(531451, 3), 1594217, 17]-NRT-code) | [i] | OOA Duplication | |
| 4 | Linear OOA(3137, 531451, F3, 3, 16) (dual of [(531451, 3), 1594216, 17]-NRT-code) | [i] | ||
| 5 | Linear OOA(3135, 468441, F3, 4, 16) (dual of [(468441, 4), 1873629, 17]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 6 | Linear OOA(3135, 468441, F3, 5, 16) (dual of [(468441, 5), 2342070, 17]-NRT-code) | [i] | ||
| 7 | Digital (119, 135, 468441)-net over F3 | [i] | ||