Information on Result #676111
Linear OA(3172, 2239, F3, 34) (dual of [2239, 2067, 35]-code), using construction X applied to Ce(33) ⊂ Ce(25) based on
- linear OA(3155, 2187, F3, 34) (dual of [2187, 2032, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(3120, 2187, F3, 26) (dual of [2187, 2067, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(317, 52, F3, 7) (dual of [52, 35, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(317, 80, F3, 7) (dual of [80, 63, 8]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 80 = 34−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 8 [i]
- discarding factors / shortening the dual code based on linear OA(317, 80, F3, 7) (dual of [80, 63, 8]-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 OOA(3172, 2237, F3, 2, 34) (dual of [(2237, 2), 4302, 35]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3172, 2237, F3, 3, 34) (dual of [(2237, 3), 6539, 35]-NRT-code) | [i] | ||
| 3 | Linear OOA(3172, 2237, F3, 4, 34) (dual of [(2237, 4), 8776, 35]-NRT-code) | [i] | ||
| 4 | Linear OOA(3172, 2237, F3, 5, 34) (dual of [(2237, 5), 11013, 35]-NRT-code) | [i] | ||
| 5 | Digital (138, 172, 2237)-net over F3 | [i] | ||