Information on Result #704241
Linear OA(382, 769, F3, 18) (dual of [769, 687, 19]-code), using construction XX applied to C1 = C([722,9]), C2 = C([0,12]), C3 = C1 + C2 = C([0,9]), and C∩ = C1 ∩ C2 = C([722,12]) 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 = {−6,−5,…,9}, and designed minimum distance d ≥ |I|+1 = 17 [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(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 = {−6,−5,…,12}, and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(337, 728, F3, 10) (dual of [728, 691, 11]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [0,9], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(38, 28, F3, 5) (dual of [28, 20, 6]-code), using
- dual code (with bound on d by construction Y1) [i] based on
- linear OA(31, 13, F3, 1) (dual of [13, 12, 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(382, 384, F3, 2, 18) (dual of [(384, 2), 686, 19]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(382, 256, F3, 3, 18) (dual of [(256, 3), 686, 19]-NRT-code) | [i] | ||