Information on Result #677642
Linear OA(372, 85, F3, 44) (dual of [85, 13, 45]-code), using construction XX applied to C1 = C([0,81]), C2 = C([1,87]), C3 = C1 + C2 = C([1,81]), and C∩ = C1 ∩ C2 = C([0,87]) based on
- linear OA(366, 80, F3, 41) (dual of [80, 14, 42]-code), using contraction [i] 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(369, 80, F3, 43) (dual of [80, 11, 44]-code), using contraction [i] based on linear OA(3149, 160, F3, 87) (dual of [160, 11, 88]-code), using the narrow-sense BCH-code C(I) with length 160 | 38−1, defining interval I = [1,87], and designed minimum distance d ≥ |I|+1 = 88 [i]
- linear OA(370, 80, F3, 44) (dual of [80, 10, 45]-code), using contraction [i] based on linear OA(3150, 160, F3, 89) (dual of [160, 10, 90]-code), using the expurgated narrow-sense BCH-code C(I) with length 160 | 38−1, defining interval I = [0,87], and minimum distance d ≥ |{−1,0,…,87}|+1 = 90 (BCH-bound) [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(30, 1, F3, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [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(3149, 162, F3, 84) (dual of [162, 13, 85]-code) | [i] | Juxtaposition | |
| 2 | Linear OA(3150, 163, F3, 85) (dual of [163, 13, 86]-code) | [i] | ||
| 3 | Linear OA(3151, 164, F3, 86) (dual of [164, 13, 87]-code) | [i] | ||