Information on Result #704494
Linear OA(3126, 770, F3, 29) (dual of [770, 644, 30]-code), using construction XX applied to C1 = C([337,363]), C2 = C([343,365]), C3 = C1 + C2 = C([343,363]), and C∩ = C1 ∩ C2 = C([337,365]) based on
- linear OA(3108, 728, F3, 27) (dual of [728, 620, 28]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {337,338,…,363}, and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(391, 728, F3, 23) (dual of [728, 637, 24]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {343,344,…,365}, and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(3115, 728, F3, 29) (dual of [728, 613, 30]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {337,338,…,365}, and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(384, 728, F3, 21) (dual of [728, 644, 22]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {343,344,…,363}, and designed minimum distance d ≥ |I|+1 = 22 [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, 8, F3, 1) (dual of [8, 7, 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(3126, 385, F3, 2, 29) (dual of [(385, 2), 644, 30]-NRT-code) | [i] | OOA Folding | |