Information on Result #705380
Linear OA(3208, 772, F3, 50) (dual of [772, 564, 51]-code), using construction XX applied to C1 = C([722,40]), C2 = C([0,43]), C3 = C1 + C2 = C([0,40]), and C∩ = C1 ∩ C2 = C([722,43]) based on
- linear OA(3184, 728, F3, 47) (dual of [728, 544, 48]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {−6,−5,…,40}, and designed minimum distance d ≥ |I|+1 = 48 [i]
- linear OA(3172, 728, F3, 44) (dual of [728, 556, 45]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [0,43], and designed minimum distance d ≥ |I|+1 = 45 [i]
- linear OA(3196, 728, F3, 50) (dual of [728, 532, 51]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {−6,−5,…,43}, and designed minimum distance d ≥ |I|+1 = 51 [i]
- linear OA(3160, 728, F3, 41) (dual of [728, 568, 42]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [0,40], and designed minimum distance d ≥ |I|+1 = 42 [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(3208, 386, F3, 2, 50) (dual of [(386, 2), 564, 51]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(3208, 257, F3, 3, 50) (dual of [(257, 3), 563, 51]-NRT-code) | [i] | ||