Information on Result #704584
Linear OA(3139, 777, F3, 32) (dual of [777, 638, 33]-code), using construction XX applied to C1 = C([336,363]), C2 = C([342,367]), C3 = C1 + C2 = C([342,363]), and C∩ = C1 ∩ C2 = C([336,367]) 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(3103, 728, F3, 26) (dual of [728, 625, 27]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {342,343,…,367}, and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(3124, 728, F3, 32) (dual of [728, 604, 33]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {336,337,…,367}, and designed minimum distance d ≥ |I|+1 = 33 [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(35, 18, F3, 3) (dual of [18, 13, 4]-code or 18-cap in PG(4,3)), using
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(3140, 778, F3, 32) (dual of [778, 638, 33]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(3139, 259, F3, 3, 32) (dual of [(259, 3), 638, 33]-NRT-code) | [i] | OOA Folding | |