Information on Result #704466
Linear OA(3121, 772, F3, 28) (dual of [772, 651, 29]-code), using construction XX applied to C1 = C([722,18]), C2 = C([0,21]), C3 = C1 + C2 = C([0,18]), and C∩ = C1 ∩ C2 = C([722,21]) based on
- linear OA(397, 728, F3, 25) (dual of [728, 631, 26]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {−6,−5,…,18}, and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(385, 728, F3, 22) (dual of [728, 643, 23]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [0,21], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(3109, 728, F3, 28) (dual of [728, 619, 29]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {−6,−5,…,21}, and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(373, 728, F3, 19) (dual of [728, 655, 20]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [0,18], and designed minimum distance d ≥ |I|+1 = 20 [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(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
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(3121, 386, F3, 2, 28) (dual of [(386, 2), 651, 29]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(3121, 257, F3, 3, 28) (dual of [(257, 3), 650, 29]-NRT-code) | [i] | ||