Information on Result #677594
Linear OA(3142, 157, F3, 79) (dual of [157, 15, 80]-code), using construction X applied to C([1,159]) ⊂ C([1,81]) based on
- linear OA(379, 80, F3, 79) (dual of [80, 1, 80]-code or 80-arc in PG(78,3)), using contraction [i] based on linear OA(3159, 160, F3, 159) (dual of [160, 1, 160]-code or 160-arc in PG(158,3)), using the narrow-sense BCH-code C(I) with length 160 | 38−1, defining interval I = [1,159], and designed minimum distance d ≥ |I|+1 = 160 [i]
- linear OA(365, 80, F3, 40) (dual of [80, 15, 41]-code), using contraction [i] based on 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(363, 77, F3, 38) (dual of [77, 14, 39]-code), using
- discarding factors / shortening the dual code based on linear OA(363, 79, F3, 38) (dual of [79, 16, 39]-code), using
- 3 times truncation [i] based on linear OA(366, 82, F3, 41) (dual of [82, 16, 42]-code), using
- discarding factors / shortening the dual code based on linear OA(363, 79, F3, 38) (dual of [79, 16, 39]-code), 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 OOA(3142, 78, F3, 2, 79) (dual of [(78, 2), 14, 80]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(3142, 52, F3, 3, 79) (dual of [(52, 3), 14, 80]-NRT-code) | [i] | ||