Information on Result #676215
Linear OA(3122, 2197, F3, 26) (dual of [2197, 2075, 27]-code), using construction XX applied to Ce(25) ⊂ Ce(24) ⊂ Ce(22) based on
- 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(3113, 2187, F3, 25) (dual of [2187, 2074, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(3106, 2187, F3, 23) (dual of [2187, 2081, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(30, 8, F3, 0) (dual of [8, 8, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(30, s, F3, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(31, 2, F3, 1) (dual of [2, 1, 2]-code), using
- dual of repetition code with length 2 [i]
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(3122, 1225, F3, 2, 26) (dual of [(1225, 2), 2328, 27]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3122, 1225, F3, 3, 26) (dual of [(1225, 3), 3553, 27]-NRT-code) | [i] | ||
| 3 | Linear OOA(3122, 1225, F3, 4, 26) (dual of [(1225, 4), 4778, 27]-NRT-code) | [i] | ||
| 4 | Linear OOA(3122, 1225, F3, 5, 26) (dual of [(1225, 5), 6003, 27]-NRT-code) | [i] | ||
| 5 | Digital (96, 122, 1225)-net over F3 | [i] | ||
| 6 | Linear OOA(3122, 732, F3, 3, 26) (dual of [(732, 3), 2074, 27]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(3122, 549, F3, 4, 26) (dual of [(549, 4), 2074, 27]-NRT-code) | [i] | ||