Information on Result #612509
Linear OA(3147, 162, F3, 83) (dual of [162, 15, 84]-code), using construction X applied to C([0,81]) ⊂ C([1,81]) based on
- linear OA(3146, 160, F3, 83) (dual of [160, 14, 84]-code), using the expurgated narrow-sense BCH-code C(I) with length 160 | 38−1, defining interval I = [0,81], and minimum distance d ≥ |{−1,0,…,81}|+1 = 84 (BCH-bound) [i]
- linear OA(3145, 160, F3, 81) (dual of [160, 15, 82]-code), using the narrow-sense BCH-code C(I) with length 160 | 38−1, defining interval I = [1,81], and designed minimum distance d ≥ |I|+1 = 82 [i]
- linear OA(31, 2, F3, 1) (dual of [2, 1, 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.
Compare with Markus Grassl’s online database of code parameters.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OA(3146, 161, F3, 82) (dual of [161, 15, 83]-code) | [i] | Truncation | |
| 2 | Linear OOA(3147, 81, F3, 2, 83) (dual of [(81, 2), 15, 84]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(3147, 54, F3, 3, 83) (dual of [(54, 3), 15, 84]-NRT-code) | [i] | ||