Information on Result #676146
Linear OA(3227, 2197, F3, 49) (dual of [2197, 1970, 50]-code), using construction XX applied to Ce(48) ⊂ Ce(46) ⊂ Ce(45) based on
- linear OA(3225, 2187, F3, 49) (dual of [2187, 1962, 50]-code), using an extension Ce(48) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,48], and designed minimum distance d ≥ |I|+1 = 49 [i]
- linear OA(3218, 2187, F3, 47) (dual of [2187, 1969, 48]-code), using an extension Ce(46) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,46], and designed minimum distance d ≥ |I|+1 = 47 [i]
- linear OA(3211, 2187, F3, 46) (dual of [2187, 1976, 47]-code), using an extension Ce(45) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,45], and designed minimum distance d ≥ |I|+1 = 46 [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(3227, 1765, F3, 2, 49) (dual of [(1765, 2), 3303, 50]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3227, 1765, F3, 3, 49) (dual of [(1765, 3), 5068, 50]-NRT-code) | [i] | ||
| 3 | Linear OOA(3227, 1765, F3, 4, 49) (dual of [(1765, 4), 6833, 50]-NRT-code) | [i] | ||
| 4 | Linear OOA(3227, 1765, F3, 5, 49) (dual of [(1765, 5), 8598, 50]-NRT-code) | [i] | ||
| 5 | Digital (178, 227, 1765)-net over F3 | [i] | ||
| 6 | Linear OOA(3227, 1098, F3, 2, 49) (dual of [(1098, 2), 1969, 50]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(3227, 732, F3, 3, 49) (dual of [(732, 3), 1969, 50]-NRT-code) | [i] | ||
| 8 | Linear OOA(3227, 549, F3, 4, 49) (dual of [(549, 4), 1969, 50]-NRT-code) | [i] | ||