Information on Result #676182
Linear OA(3171, 2197, F3, 37) (dual of [2197, 2026, 38]-code), using construction XX applied to Ce(36) ⊂ Ce(34) ⊂ Ce(33) based on
- linear OA(3169, 2187, F3, 37) (dual of [2187, 2018, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(3162, 2187, F3, 35) (dual of [2187, 2025, 36]-code), using an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
- 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(31, 9, F3, 1) (dual of [9, 8, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- linear OA(30, 1, F3, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [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(3171, 1412, F3, 2, 37) (dual of [(1412, 2), 2653, 38]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3171, 1412, F3, 3, 37) (dual of [(1412, 3), 4065, 38]-NRT-code) | [i] | ||
| 3 | Linear OOA(3171, 1412, F3, 4, 37) (dual of [(1412, 4), 5477, 38]-NRT-code) | [i] | ||
| 4 | Linear OOA(3171, 1412, F3, 5, 37) (dual of [(1412, 5), 6889, 38]-NRT-code) | [i] | ||
| 5 | Digital (134, 171, 1412)-net over F3 | [i] | ||
| 6 | Linear OOA(3171, 1098, F3, 2, 37) (dual of [(1098, 2), 2025, 38]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(3171, 732, F3, 3, 37) (dual of [(732, 3), 2025, 38]-NRT-code) | [i] | ||
| 8 | Linear OOA(3171, 549, F3, 4, 37) (dual of [(549, 4), 2025, 38]-NRT-code) | [i] | ||