Information on Result #704299
Linear OA(378, 751, F3, 19) (dual of [751, 673, 20]-code), using construction XX applied to C1 = C([725,13]), C2 = C([0,15]), C3 = C1 + C2 = C([0,13]), and C∩ = C1 ∩ C2 = C([725,15]) based on
- 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(361, 728, F3, 16) (dual of [728, 667, 17]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [0,15], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(373, 728, F3, 19) (dual of [728, 655, 20]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {−3,−2,…,15}, and designed minimum distance d ≥ |I|+1 = 20 [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(34, 16, F3, 2) (dual of [16, 12, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(34, 40, F3, 2) (dual of [40, 36, 3]-code), using
- Hamming code H(4,3) [i]
- discarding factors / shortening the dual code based on linear OA(34, 40, F3, 2) (dual of [40, 36, 3]-code), using
- linear OA(31, 7, F3, 1) (dual of [7, 6, 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
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(378, 375, F3, 2, 19) (dual of [(375, 2), 672, 20]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(378, 250, F3, 3, 19) (dual of [(250, 3), 672, 20]-NRT-code) | [i] | ||