Information on Result #2265662
Linear OA(378, 269, F3, 22) (dual of [269, 191, 23]-code), using 1 times code embedding in larger space based on linear OA(377, 268, F3, 22) (dual of [268, 191, 23]-code), using
- construction XX applied to C1 = C([239,15]), C2 = C([0,18]), C3 = C1 + C2 = C([0,15]), and C∩ = C1 ∩ C2 = C([239,18]) [i] based on
- linear OA(361, 242, F3, 19) (dual of [242, 181, 20]-code), using the primitive BCH-code C(I) with length 242 = 35−1, defining interval I = {−3,−2,…,15}, and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(361, 242, F3, 19) (dual of [242, 181, 20]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 242 = 35−1, defining interval I = [0,18], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(371, 242, F3, 22) (dual of [242, 171, 23]-code), using the primitive BCH-code C(I) with length 242 = 35−1, defining interval I = {−3,−2,…,18}, and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(351, 242, F3, 16) (dual of [242, 191, 17]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 242 = 35−1, defining interval I = [0,15], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(33, 13, F3, 2) (dual of [13, 10, 3]-code), using
- Hamming code H(3,3) [i]
- linear OA(33, 13, F3, 2) (dual of [13, 10, 3]-code) (see above)
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.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(378, 269, F3, 2, 22) (dual of [(269, 2), 460, 23]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(378, 269, F3, 3, 22) (dual of [(269, 3), 729, 23]-NRT-code) | [i] | ||
| 3 | Linear OOA(378, 269, F3, 4, 22) (dual of [(269, 4), 998, 23]-NRT-code) | [i] | ||
| 4 | Linear OOA(378, 269, F3, 5, 22) (dual of [(269, 5), 1267, 23]-NRT-code) | [i] | ||
| 5 | Digital (56, 78, 269)-net over F3 | [i] | ||