Information on Result #705051
Linear OA(3186, 796, F3, 43) (dual of [796, 610, 44]-code), using construction XX applied to C1 = C([722,30]), C2 = C([0,36]), C3 = C1 + C2 = C([0,30]), and C∩ = C1 ∩ C2 = C([722,36]) based on
- linear OA(3142, 728, F3, 37) (dual of [728, 586, 38]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {−6,−5,…,30}, and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(3142, 728, F3, 37) (dual of [728, 586, 38]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [0,36], and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(3166, 728, F3, 43) (dual of [728, 562, 44]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {−6,−5,…,36}, and designed minimum distance d ≥ |I|+1 = 44 [i]
- linear OA(3118, 728, F3, 31) (dual of [728, 610, 32]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [0,30], and designed minimum distance d ≥ |I|+1 = 32 [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(310, 34, F3, 5) (dual of [34, 24, 6]-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 OA(3187, 797, F3, 43) (dual of [797, 610, 44]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(3188, 798, F3, 43) (dual of [798, 610, 44]-code) | [i] | ||
| 3 | Linear OA(3189, 799, F3, 43) (dual of [799, 610, 44]-code) | [i] | ||
| 4 | Linear OA(3185, 795, F3, 42) (dual of [795, 610, 43]-code) | [i] | Truncation | |
| 5 | Linear OOA(3186, 398, F3, 2, 43) (dual of [(398, 2), 610, 44]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(3186, 265, F3, 3, 43) (dual of [(265, 3), 609, 44]-NRT-code) | [i] | ||