Information on Result #952574
Linear OOA(3146, 1594334, F3, 3, 16) (dual of [(1594334, 3), 4782856, 17]-NRT-code), using OOA 3-folding based on linear OA(3146, 4783002, F3, 16) (dual of [4783002, 4782856, 17]-code), using
- 1 times code embedding in larger space [i] based on linear OA(3145, 4783001, F3, 16) (dual of [4783001, 4782856, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(12) [i] based on
- linear OA(3141, 4782969, F3, 16) (dual of [4782969, 4782828, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(3113, 4782969, F3, 13) (dual of [4782969, 4782856, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(34, 32, F3, 2) (dual of [32, 28, 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(3146, 1594334, F3, 3, 15) (dual of [(1594334, 3), 4782856, 16]-NRT-code) | [i] | Strength Reduction for OOAs | |
| 2 | Linear OOA(3147, 1594334, F3, 3, 16) (dual of [(1594334, 3), 4782855, 17]-NRT-code) | [i] | OOA Duplication | |
| 3 | Linear OOA(3148, 1594334, F3, 3, 16) (dual of [(1594334, 3), 4782854, 17]-NRT-code) | [i] | ||
| 4 | Linear OOA(3146, 1282397, F3, 4, 16) (dual of [(1282397, 4), 5129442, 17]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 5 | Linear OOA(3146, 1282397, F3, 5, 16) (dual of [(1282397, 5), 6411839, 17]-NRT-code) | [i] | ||
| 6 | Digital (130, 146, 1282397)-net over F3 | [i] | ||