Information on Result #633017
Linear OA(3182, 410, F3, 51) (dual of [410, 228, 52]-code), using concatenation of two codes based on
- linear OA(8125, 82, F81, 25) (dual of [82, 57, 26]-code or 82-arc in PG(24,81)), using
- extended Reed–Solomon code RSe(57,81) [i]
- the expurgated narrow-sense BCH-code C(I) with length 82 | 812−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(31, 5, F3, 1) (dual of [5, 4, 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
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(3182, 410, F3, 50) (dual of [410, 228, 51]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(3183, 411, F3, 51) (dual of [411, 228, 52]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(3184, 412, F3, 51) (dual of [412, 228, 52]-code) | [i] | ||
| 4 | Linear OA(3185, 413, F3, 51) (dual of [413, 228, 52]-code) | [i] | ||
| 5 | Linear OA(3186, 414, F3, 51) (dual of [414, 228, 52]-code) | [i] | ||
| 6 | Linear OA(3187, 415, F3, 51) (dual of [415, 228, 52]-code) | [i] | ||
| 7 | Linear OA(3181, 409, F3, 50) (dual of [409, 228, 51]-code) | [i] | Truncation | |
| 8 | Linear OOA(3182, 205, F3, 2, 51) (dual of [(205, 2), 228, 52]-NRT-code) | [i] | OOA Folding | |
| 9 | Linear OOA(3182, 136, F3, 3, 51) (dual of [(136, 3), 226, 52]-NRT-code) | [i] | ||