Information on Result #677599
Linear OA(389, 96, F3, 58) (dual of [96, 7, 59]-code), using construction XX applied to C([1,159]) ⊂ C([1,105]) ⊂ 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(375, 80, F3, 52) (dual of [80, 5, 53]-code), using contraction [i] based on linear OA(3155, 160, F3, 105) (dual of [160, 5, 106]-code), using the narrow-sense BCH-code C(I) with length 160 | 38−1, defining interval I = [1,105], and designed minimum distance d ≥ |I|+1 = 106 [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(36, 12, F3, 5) (dual of [12, 6, 6]-code), using
- extended Golay code Ge(3) [i]
- 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]
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(389, 96, F3, 57) (dual of [96, 7, 58]-code) | [i] | Strength Reduction | |
| 2 | Linear OOA(389, 48, F3, 2, 58) (dual of [(48, 2), 7, 59]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(389, 32, F3, 3, 58) (dual of [(32, 3), 7, 59]-NRT-code) | [i] | ||