Information on Result #705697
Linear OA(3210, 743, F3, 53) (dual of [743, 533, 54]-code), using construction XX applied to C1 = C([727,49]), C2 = C([1,51]), C3 = C1 + C2 = C([1,49]), and C∩ = C1 ∩ C2 = C([727,51]) based on
- linear OA(3202, 728, F3, 51) (dual of [728, 526, 52]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {−1,0,…,49}, and designed minimum distance d ≥ |I|+1 = 52 [i]
- linear OA(3201, 728, F3, 51) (dual of [728, 527, 52]-code), using the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,51], and designed minimum distance d ≥ |I|+1 = 52 [i]
- linear OA(3208, 728, F3, 53) (dual of [728, 520, 54]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {−1,0,…,51}, and designed minimum distance d ≥ |I|+1 = 54 [i]
- linear OA(3195, 728, F3, 49) (dual of [728, 533, 50]-code), using the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,49], and designed minimum distance d ≥ |I|+1 = 50 [i]
- linear OA(31, 8, F3, 1) (dual of [8, 7, 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
- 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 (see above)
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(3210, 371, F3, 2, 53) (dual of [(371, 2), 532, 54]-NRT-code) | [i] | OOA Folding | |