Information on Result #633616
Linear OA(3238, 410, F3, 79) (dual of [410, 172, 80]-code), using concatenation of two codes based on
- linear OA(8139, 82, F81, 39) (dual of [82, 43, 40]-code or 82-arc in PG(38,81)), using
- extended Reed–Solomon code RSe(43,81) [i]
- the expurgated narrow-sense BCH-code C(I) with length 82 | 812−1, defining interval I = [0,19], and minimum distance d ≥ |{−19,−18,…,19}|+1 = 40 (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(3238, 410, F3, 78) (dual of [410, 172, 79]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(3239, 411, F3, 79) (dual of [411, 172, 80]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(3240, 412, F3, 79) (dual of [412, 172, 80]-code) | [i] | ||
| 4 | Linear OA(3241, 413, F3, 79) (dual of [413, 172, 80]-code) | [i] | ||
| 5 | Linear OA(3242, 414, F3, 79) (dual of [414, 172, 80]-code) | [i] | ||
| 6 | Linear OA(3243, 415, F3, 79) (dual of [415, 172, 80]-code) | [i] | ||
| 7 | Linear OA(3237, 409, F3, 78) (dual of [409, 172, 79]-code) | [i] | Truncation | |
| 8 | Linear OOA(3238, 205, F3, 2, 79) (dual of [(205, 2), 172, 80]-NRT-code) | [i] | OOA Folding | |
| 9 | Linear OOA(3238, 136, F3, 3, 79) (dual of [(136, 3), 170, 80]-NRT-code) | [i] | ||