Information on Result #676123
Linear OA(3211, 2250, F3, 41) (dual of [2250, 2039, 42]-code), using construction X applied to Ce(40) ⊂ Ce(31) based on
- linear OA(3190, 2187, F3, 41) (dual of [2187, 1997, 42]-code), using an extension Ce(40) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,40], and designed minimum distance d ≥ |I|+1 = 41 [i]
- linear OA(3148, 2187, F3, 32) (dual of [2187, 2039, 33]-code), using an extension Ce(31) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,31], and designed minimum distance d ≥ |I|+1 = 32 [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(3212, 2251, F3, 41) (dual of [2251, 2039, 42]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(3213, 2252, F3, 41) (dual of [2252, 2039, 42]-code) | [i] | ||
| 3 | Linear OOA(3211, 1125, F3, 2, 41) (dual of [(1125, 2), 2039, 42]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(3211, 750, F3, 3, 41) (dual of [(750, 3), 2039, 42]-NRT-code) | [i] | ||
| 5 | Linear OOA(3211, 562, F3, 4, 41) (dual of [(562, 4), 2037, 42]-NRT-code) | [i] | ||
| 6 | Linear OOA(3211, 450, F3, 5, 41) (dual of [(450, 5), 2039, 42]-NRT-code) | [i] | ||