Information on Result #952866
Linear OOA(3174, 1594334, F3, 3, 19) (dual of [(1594334, 3), 4782828, 20]-NRT-code), using OOA 3-folding based on linear OA(3174, 4783002, F3, 19) (dual of [4783002, 4782828, 20]-code), using
- 1 times code embedding in larger space [i] based on linear OA(3173, 4783001, F3, 19) (dual of [4783001, 4782828, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(15) [i] based on
- linear OA(3169, 4782969, F3, 19) (dual of [4782969, 4782800, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- 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(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(18) ⊂ Ce(15) [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(3174, 1594334, F3, 3, 18) (dual of [(1594334, 3), 4782828, 19]-NRT-code) | [i] | Strength Reduction for OOAs | |
| 2 | Linear OOA(3175, 1594334, F3, 3, 19) (dual of [(1594334, 3), 4782827, 20]-NRT-code) | [i] | OOA Duplication | |