Information on Result #674287
Linear OA(3145, 4783001, F3, 16) (dual of [4783001, 4782856, 17]-code), using construction X applied to Ce(15) ⊂ Ce(12) 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
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(3146, 4783002, F3, 16) (dual of [4783002, 4782856, 17]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(3147, 4783003, F3, 16) (dual of [4783003, 4782856, 17]-code) | [i] | ||
| 3 | Linear OA(3148, 4783004, F3, 16) (dual of [4783004, 4782856, 17]-code) | [i] | ||
| 4 | Linear OOA(3145, 2391500, F3, 2, 16) (dual of [(2391500, 2), 4782855, 17]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(3145, 1594333, F3, 3, 16) (dual of [(1594333, 3), 4782854, 17]-NRT-code) | [i] | ||
| 6 | Linear OOA(3145, 1195750, F3, 4, 16) (dual of [(1195750, 4), 4782855, 17]-NRT-code) | [i] | ||
| 7 | Linear OOA(3145, 956600, F3, 5, 16) (dual of [(956600, 5), 4782855, 17]-NRT-code) | [i] | ||
| 8 | Linear OOA(3145, 597875, F3, 16, 16) (dual of [(597875, 16), 9565855, 17]-NRT-code) | [i] | OA Folding and Stacking | |