Information on Result #676124
Linear OA(3204, 2250, F3, 40) (dual of [2250, 2046, 41]-code), using construction X applied to Ce(39) ⊂ Ce(30) based on
- linear OA(3183, 2187, F3, 40) (dual of [2187, 2004, 41]-code), using an extension Ce(39) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,39], and designed minimum distance d ≥ |I|+1 = 40 [i]
- linear OA(3141, 2187, F3, 31) (dual of [2187, 2046, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(321, 63, F3, 8) (dual of [63, 42, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(321, 80, F3, 8) (dual of [80, 59, 9]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 80 = 34−1, defining interval I = [0,7], and designed minimum distance d ≥ |I|+1 = 9 [i]
- discarding factors / shortening the dual code based on linear OA(321, 80, F3, 8) (dual of [80, 59, 9]-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(3205, 2251, F3, 40) (dual of [2251, 2046, 41]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(3206, 2252, F3, 40) (dual of [2252, 2046, 41]-code) | [i] | ||
| 3 | Linear OA(3207, 2253, F3, 40) (dual of [2253, 2046, 41]-code) | [i] | ||
| 4 | Linear OOA(3204, 1125, F3, 2, 40) (dual of [(1125, 2), 2046, 41]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(3204, 750, F3, 3, 40) (dual of [(750, 3), 2046, 41]-NRT-code) | [i] | ||
| 6 | Linear OOA(3204, 562, F3, 4, 40) (dual of [(562, 4), 2044, 41]-NRT-code) | [i] | ||
| 7 | Linear OOA(3204, 450, F3, 5, 40) (dual of [(450, 5), 2046, 41]-NRT-code) | [i] | ||