Information on Result #674936
Linear OA(3109, 59087, F3, 16) (dual of [59087, 58978, 17]-code), using construction X applied to Ce(15) ⊂ Ce(10) based on
- linear OA(3101, 59049, F3, 16) (dual of [59049, 58948, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(371, 59049, F3, 11) (dual of [59049, 58978, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(38, 38, F3, 4) (dual of [38, 30, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(38, 41, F3, 4) (dual of [41, 33, 5]-code), using
- the narrow-sense BCH-code C(I) with length 41 | 38−1, defining interval I = [1,1], and minimum distance d ≥ |{−3,−1,1,3}|+1 = 5 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(38, 41, F3, 4) (dual of [41, 33, 5]-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(3110, 59088, F3, 16) (dual of [59088, 58978, 17]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(3108, 59086, F3, 15) (dual of [59086, 58978, 16]-code) | [i] | Truncation | |
| 3 | Linear OOA(3109, 29543, F3, 2, 16) (dual of [(29543, 2), 58977, 17]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(3109, 19695, F3, 3, 16) (dual of [(19695, 3), 58976, 17]-NRT-code) | [i] | ||
| 5 | Linear OOA(3109, 14771, F3, 4, 16) (dual of [(14771, 4), 58975, 17]-NRT-code) | [i] | ||
| 6 | Linear OOA(3109, 11817, F3, 5, 16) (dual of [(11817, 5), 58976, 17]-NRT-code) | [i] | ||
| 7 | Linear OOA(3109, 7385, F3, 16, 16) (dual of [(7385, 16), 118051, 17]-NRT-code) | [i] | OA Folding and Stacking | |