Information on Result #704307
Linear OA(396, 769, F3, 22) (dual of [769, 673, 23]-code), using construction XX applied to C1 = C([722,13]), C2 = C([0,15]), C3 = C1 + C2 = C([0,13]), and C∩ = C1 ∩ C2 = C([722,15]) based on
- linear OA(379, 728, F3, 20) (dual of [728, 649, 21]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {−6,−5,…,13}, and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(361, 728, F3, 16) (dual of [728, 667, 17]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [0,15], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(385, 728, F3, 22) (dual of [728, 643, 23]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {−6,−5,…,15}, and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(355, 728, F3, 14) (dual of [728, 673, 15]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [0,13], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(310, 34, F3, 5) (dual of [34, 24, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(310, 36, F3, 5) (dual of [36, 26, 6]-code), using
- (u, u−v, u+v+w)-construction [i] based on
- linear OA(31, 12, F3, 1) (dual of [12, 11, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- linear OA(33, 12, F3, 2) (dual of [12, 9, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(33, 13, F3, 2) (dual of [13, 10, 3]-code), using
- Hamming code H(3,3) [i]
- discarding factors / shortening the dual code based on linear OA(33, 13, F3, 2) (dual of [13, 10, 3]-code), using
- linear OA(36, 12, F3, 5) (dual of [12, 6, 6]-code), using
- extended Golay code Ge(3) [i]
- linear OA(31, 12, F3, 1) (dual of [12, 11, 2]-code), using
- (u, u−v, u+v+w)-construction [i] based on
- discarding factors / shortening the dual code based on linear OA(310, 36, F3, 5) (dual of [36, 26, 6]-code), using
- linear OA(31, 7, F3, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s (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(396, 749, F3, 2, 22) (dual of [(749, 2), 1402, 23]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(396, 749, F3, 3, 22) (dual of [(749, 3), 2151, 23]-NRT-code) | [i] | ||
| 3 | Linear OOA(396, 749, F3, 4, 22) (dual of [(749, 4), 2900, 23]-NRT-code) | [i] | ||
| 4 | Linear OOA(396, 749, F3, 5, 22) (dual of [(749, 5), 3649, 23]-NRT-code) | [i] | ||
| 5 | Digital (74, 96, 749)-net over F3 | [i] | ||
| 6 | Linear OOA(396, 384, F3, 2, 22) (dual of [(384, 2), 672, 23]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(396, 256, F3, 3, 22) (dual of [(256, 3), 672, 23]-NRT-code) | [i] | ||