Information on Result #704612
Linear OA(3147, 785, F3, 33) (dual of [785, 638, 34]-code), using construction XX applied to C1 = C([336,363]), C2 = C([342,368]), C3 = C1 + C2 = C([342,363]), and C∩ = C1 ∩ C2 = C([336,368]) based on
- linear OA(3111, 728, F3, 28) (dual of [728, 617, 29]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {336,337,…,363}, and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(3109, 728, F3, 27) (dual of [728, 619, 28]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {342,343,…,368}, and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(3130, 728, F3, 33) (dual of [728, 598, 34]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {336,337,…,368}, and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(390, 728, F3, 22) (dual of [728, 638, 23]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {342,343,…,363}, and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(310, 31, F3, 5) (dual of [31, 21, 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(37, 26, F3, 4) (dual of [26, 19, 5]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 26 = 33−1, defining interval I = [0,2], and designed minimum distance d ≥ |I|+1 = 5 [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.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OA(3148, 786, F3, 33) (dual of [786, 638, 34]-code) | [i] | Code Embedding in Larger Space | |