Information on Result #2676891
Linear OOA(3138, 531452, F3, 3, 16) (dual of [(531452, 3), 1594218, 17]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(3135, 531451, F3, 3, 16) (dual of [(531451, 3), 1594218, 17]-NRT-code), using
- OOA 3-folding [i] 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
- construction X applied to Ce(15) ⊂ Ce(12) [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(3138, 531452, F3, 4, 16) (dual of [(531452, 4), 2125670, 17]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3138, 531452, F3, 5, 16) (dual of [(531452, 5), 2657122, 17]-NRT-code) | [i] | ||
| 3 | Digital (122, 138, 531452)-net over F3 | [i] | ||