Information on Result #700901
Linear OA(353, 130, F3, 17) (dual of [130, 77, 18]-code), using construction XX applied to C1 = C({0,1,2,4,5,7,8,10,11,40}), C2 = C([0,13]), C3 = C1 + C2 = C([0,11]), and C∩ = C1 ∩ C2 = C({0,1,2,4,5,7,8,10,11,13,40}) based on
- linear OA(346, 121, F3, 14) (dual of [121, 75, 15]-code), using the cyclic code C(A) with length 121 | 35−1, defining set A = {0,1,2,4,5,7,8,10,11,40}, and minimum distance d ≥ |{−1,0,…,12}|+1 = 15 (BCH-bound) [i]
- linear OA(346, 121, F3, 16) (dual of [121, 75, 17]-code), using the expurgated narrow-sense BCH-code C(I) with length 121 | 35−1, defining interval I = [0,13], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(351, 121, F3, 17) (dual of [121, 70, 18]-code), using the cyclic code C(A) with length 121 | 35−1, defining set A = {0,1,2,4,5,7,8,10,11,13,40}, and minimum distance d ≥ |{−1,0,…,15}|+1 = 18 (BCH-bound) [i]
- linear OA(341, 121, F3, 13) (dual of [121, 80, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 121 | 35−1, defining interval I = [0,11], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(30, 5, F3, 0) (dual of [5, 5, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(30, s, F3, 0) (dual of [s, s, 1]-code) for arbitrarily large s, 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]
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(353, 65, F3, 2, 17) (dual of [(65, 2), 77, 18]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(353, 43, F3, 3, 17) (dual of [(43, 3), 76, 18]-NRT-code) | [i] | ||