Information on Result #704253
Linear OA(370, 747, F3, 17) (dual of [747, 677, 18]-code), using construction XX applied to C1 = C([725,12]), C2 = C([0,13]), C3 = C1 + C2 = C([0,12]), and C∩ = C1 ∩ C2 = C([725,13]) based on
- linear OA(361, 728, F3, 16) (dual of [728, 667, 17]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {−3,−2,…,12}, and designed minimum distance d ≥ |I|+1 = 17 [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(367, 728, F3, 17) (dual of [728, 661, 18]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {−3,−2,…,13}, and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(349, 728, F3, 13) (dual of [728, 679, 14]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [0,12], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(33, 13, F3, 2) (dual of [13, 10, 3]-code), using
- Hamming code H(3,3) [i]
- linear OA(30, 6, F3, 0) (dual of [6, 6, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(30, s, F3, 0) (dual of [s, s, 1]-code) for arbitrarily large s, 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 OOA(370, 373, F3, 2, 17) (dual of [(373, 2), 676, 18]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(370, 249, F3, 3, 17) (dual of [(249, 3), 677, 18]-NRT-code) | [i] | ||
| 3 | Linear OOA(370, 186, F3, 4, 17) (dual of [(186, 4), 674, 18]-NRT-code) | [i] | ||