Information on Result #677578
Linear OA(3105, 112, F3, 67) (dual of [112, 7, 68]-code), using construction X applied to C([1,159]) ⊂ C([1,99]) 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(373, 80, F3, 49) (dual of [80, 7, 50]-code), using contraction [i] based on linear OA(3153, 160, F3, 99) (dual of [160, 7, 100]-code), using the narrow-sense BCH-code C(I) with length 160 | 38−1, defining interval I = [1,99], and designed minimum distance d ≥ |I|+1 = 100 [i]
- linear OA(326, 32, F3, 17) (dual of [32, 6, 18]-code), using
- concatenation of two codes [i] based on
- linear OA(95, 8, F9, 5) (dual of [8, 3, 6]-code or 8-arc in PG(4,9)), using
- discarding factors / shortening the dual code based on linear OA(95, 9, F9, 5) (dual of [9, 4, 6]-code or 9-arc in PG(4,9)), using
- Reed–Solomon code RS(4,9) [i]
- discarding factors / shortening the dual code based on linear OA(95, 9, F9, 5) (dual of [9, 4, 6]-code or 9-arc in PG(4,9)), using
- linear OA(32, 4, F3, 2) (dual of [4, 2, 3]-code or 4-arc in PG(1,3)), using
- extended Reed–Solomon code RSe(2,3) [i]
- Hamming code H(2,3) [i]
- Simplex code S(2,3) [i]
- the Tetracode [i]
- linear OA(95, 8, F9, 5) (dual of [8, 3, 6]-code or 8-arc in PG(4,9)), using
- concatenation of two codes [i] based on
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(3105, 112, F3, 66) (dual of [112, 7, 67]-code) | [i] | Strength Reduction | |