Information on Result #675197
Linear OA(399, 19718, F3, 16) (dual of [19718, 19619, 17]-code), using construction X applied to Ce(15) ⊂ Ce(10) based on
- linear OA(391, 19683, F3, 16) (dual of [19683, 19592, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(364, 19683, F3, 11) (dual of [19683, 19619, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(38, 35, F3, 4) (dual of [35, 27, 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(3100, 19719, F3, 16) (dual of [19719, 19619, 17]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(398, 19717, F3, 15) (dual of [19717, 19619, 16]-code) | [i] | Truncation | |
| 3 | Linear OOA(399, 9859, F3, 2, 16) (dual of [(9859, 2), 19619, 17]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(399, 6572, F3, 3, 16) (dual of [(6572, 3), 19617, 17]-NRT-code) | [i] | ||
| 5 | Linear OOA(399, 4929, F3, 4, 16) (dual of [(4929, 4), 19617, 17]-NRT-code) | [i] | ||
| 6 | Linear OOA(399, 3943, F3, 5, 16) (dual of [(3943, 5), 19616, 17]-NRT-code) | [i] | ||
| 7 | Linear OOA(399, 2464, F3, 16, 16) (dual of [(2464, 16), 39325, 17]-NRT-code) | [i] | OA Folding and Stacking | |