Information on Result #674259
Linear OA(3142, 4782984, F3, 16) (dual of [4782984, 4782842, 17]-code), using construction X applied to Ce(15) ⊂ Ce(13) 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(3127, 4782969, F3, 14) (dual of [4782969, 4782842, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(31, 15, F3, 1) (dual of [15, 14, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, 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 OA(3143, 4782985, F3, 16) (dual of [4782985, 4782842, 17]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(3144, 4782986, F3, 16) (dual of [4782986, 4782842, 17]-code) | [i] | ||
| 3 | Linear OOA(3142, 2391492, F3, 2, 16) (dual of [(2391492, 2), 4782842, 17]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(3142, 1594328, F3, 3, 16) (dual of [(1594328, 3), 4782842, 17]-NRT-code) | [i] | ||
| 5 | Linear OOA(3142, 1195746, F3, 4, 16) (dual of [(1195746, 4), 4782842, 17]-NRT-code) | [i] | ||
| 6 | Linear OOA(3142, 956596, F3, 5, 16) (dual of [(956596, 5), 4782838, 17]-NRT-code) | [i] | ||
| 7 | Linear OOA(3142, 597873, F3, 16, 16) (dual of [(597873, 16), 9565826, 17]-NRT-code) | [i] | OA Folding and Stacking | |